Degrading processes of material

Study Support

Bohumír Strnadel

Ostrava 2015

VŠB – TECHNICAL UNIVERSITY OF OSTRAVA

FACULTY OF METALLURGY AND MATERIALS ENGINEERING

Title: Degrading processes of material

Code:

Author: Bohumír Strnadel

Edition: first, 2015

Number of pages: 55

Academic materials for the Materials Engineering Systems study programme at the

Faculty of Metallurgy and Materials Engineering.

Proofreading has not been performed.

Execution: VŠB - Technical University of Ostrava

1. Introduction

Study time Not specified – the goal of this chapter is to introduce the issues of

material degradation processes to the students

Objective After reading this chapter, the reader should be prepared to study the

following chapters

Explication

Utility characteristics of constructional materials do not stay unchanged during the use of

the machines. The degrading processes happen as a result of a long time effecting of a stress-

deformation field, temperature, force effects of functional surfaces, or chemical effects of the

surrounding environment. The characteristics of the material degrade with the changes of the

structure. The effects of the degrading processes depend usually on time; a risk of their

failure grows with a growing period of the use of the constructional parts, even though the

conditions of operation remain the same.

The durability of the construction materials against the effects of the degrading processes

can be evaluated basically in two ways. The first way is based on the direct evaluation of the

dependence of the mechanical characteristics of the material on time; the characteristics are

set and based on various conditions of stress. These results can be used for a specific technical

application of the material, under the conditions of effects of other factors. This helps us to set

the moment of emergence of the ultimate state of the construction parts or to evaluate the

residual durability of the machines and devices. The results of the second way of evaluation

are local characteristics of the damage of the material, which represent the endurance of the

microstructure against the initiation of the localised ultimate state. Even though the evaluation

of the changes of the mechanical characteristics as the result of the degrading processes is

usually adequate during making of concepts of the suitable material for the production of the

construction part, the evaluation of the relations between the mechanism of the degrading

process, microstructure parameters and mechanical characteristics of the material is inevitable

for a systematic development of new types of construction materials with higher level of

utility characteristics. Because the state of the microstructure is the result of the constitution

of the material and of the technology of its production and processing, technological

parameters have to be evaluated during the final evaluation of the durability of the material

against emergence of the degrading process.

Most of degrading processes culminate during the break of the constructional part, which

forms two new free surfaces (fig. 1) in the structure of the material under the influence of the

stress. Low energy brittle fracture happens without a continuous, plastic deformation, directly

by tampering of the inter-atom bindings, as it is by glass, or ceramics. Defects of the structure,

pores, cavities or micro breaches can significantly simplify the process of the brittle fracture,

because of the concentration of the stress in their environment.

Time dependent permanent plastic

deformation of the constructional

materials can also be caused by long-term

effecting be it low stress at higher or high

temperatures. The degrading process,

which can emerge during these conditions,

creep, is made by similar mechanism as

by form breach. Both intercrystalline and

transcrystalline creep break can emerge in

metals, the mechanisms of

transcrystallilne creep are repressed with

according conditions for transcrystalline

fission in most ceramic materials.

There are other degrading processes dependent on time besides the creep mechanisms of

damage. Thermoplastics act as viscose matter during higher temperatures and low speeds of

deformation and they almost become liquid in their behaviour, they are, in opposite, at low

temperatures linearly elastic and they have the characteristics which are similar to the glass.

The character of the fracture processes of thermoplastics depends on the temperature. The

brittle fracture is created at sufficient low temperatures; this is prevented by the emergence of

Fig. 1 The initiation of the brittle fracture in carbon

steel (with the consent of the author Doc. Ing. Ivo

Dlouhý, CSc. from ÚFM AV ČR Brno).

10 m

the belt skid. The prolonging of the structure of the thermoplastics and the final forming

fracture happen above the temperature of glass changeover at higher level of stress.

Stressing of the material at high speeds of deformation, when it is necessary to count with

the effects of the stress waves, leads to narrowly localized elasto-plastic deformation, often by

simultaneous extreme increase of the temperature. The influence of high speed of the

deformation on the character of the fracture breach depends on the conditions of the evolving

of the plastic deformation. The materials sensitive to the speed of the deformation, like carbon

steel, are usually breached by the dynamic breach fracture, when dynamic forming fracture

happens in the materials with high persistence.

One of very important degrading process is a fatigue damage of the constructional

materials. This happens as the result of effecting of the part of the stress changeable in time.

High level of amplitude of stress, which causes major plastic deformation leads to low-cycle

fatigue. Low amplitude of stress, accompanied by mostly elastic deformation, leads, on the

other hand, to a high-cycle fatigue. The process of the fatigue damage and the character of

the fracture surfaces depends not only on the microstructure of the material, but also on many

other factors connected, not only to the way of straining, but also to the conditions of the

environment.

The degrading processes created by the chemical interaction of the material and

surrounding environment, do not only depreciate the surface layers, but also often its inner

structure, these processes are called corrosion. Basically there are two basic types of

corrosion. A special type of the degrading process is radiation damage, caused by the

interaction of strong stream of radiation and the structure of the construction material.

Radiation and especially neutron radiation at high integral flow of neutrons cause radiation

firming and fragility of steels. These processes have the effect of decreasing of reliability and

safety of the operating of nuclear energy devices.

.

The processes of abrasion can be qualified as unwanted changes of the surface or

measures of solid figures, which are caused either by a mutual interaction of the functional

surfaces or the functional surface and a medium, which causes the abrasion. The abrasion

manifests itself as a disposing or moving of the particles of matter from the functional surface,

which is commonly accompanied also by other chemical or electrochemical processes. The

original causes of the adhesive abrasion are inequalities of functional surfaces, which are in

mutual relative motion by the pressure force. Abrasive abrasion is created as the result of

force interaction of functional surface of one body with the surface inequalities of the other

body, or solid particles of solid phase during their mutual shear motion. Volume abrasion

manifests itself by scratching and grooving into the functional surface, these then lead to the

limiting or to the complete loss of the function of the constructional part. Erosive abrasion is

created by the interaction of the particles of the solid phase, often taken by liquid or gaseous

media and the functional surface of the constructional parts. The erosion can be created at

high speeds of flowing medium, also without the presence of the erosive particles. The

erosion displays itself on the functional surface often by an unequal scouring of the surface

layers of the material and by grooving caused by the turbulences of the flowing media.

Cavitation abrasion is often created by repeated creation and quick destruction (implosion) of

bubbles on the surface of such constructional parts, which are in contact with the flowing

liquid. The repeated implosion of the bubbles leads to the creation of hydrodynamic pushes

and to a localised plastic deformation, which results in the creation of sub-surface micro

fractures and dividing of the matters of the material from the functional surface.

Fatigue abrasion, sometimes called contact abrasion, is created on functional surfaces,

which are exposed to repeated pressure stress during a rolling motion. Changing elastic and

elastic-plastic deformations happen in the surface layers of such subjected material; these

deformations can initiate sub-surface micro fractures depending on the value of the ongoing

tension.

Searching of the dependence between the micro structure, characteristics and the way of

stress and abrasion of functional surfaces of the constructional parts is, with regards to the

number of the factors, which the processes influence, often very difficult. It is suitable to

examine whole constructional parts by the simulation of operating stress in some cases. The

knowledge of the procedure of the degrading processes majorly influences the creation of the

criteria of the choice of the constructional material for a given purpose of use. The ultimate

stress-deformational characteristics, fracture persistence, or the parameters of the limit

damage of the material determine the maximum allowed stress of the constructional part. The

criteria of the proposition of the constructional material is then, along with the form design of

the functional part, the condition of the minimum of its weight and economical conditions, the

way for optimal choice of the constructional material. The proposition of the material

becomes eventually also the matter of the structural design, which is a necessary condition for

the use of their characteristics, especially in new progressive types of materials, such as

composites. The evaluation of the phase structural characteristics of the material creates a line

connecting design of the inner construction of the material with the form design of the

functional part, which is produced from such material, in direct link to the development of the

WEAR processes and to the methods of optimized proposition of the material for given

intention of use.

Summary of terms

After reading this chapter, the reader should understand the following terms:

Basic mechanical properties of materials

Describe the degradation processes of materials

Understanding the links between the utility properties and microstructure of material

Questions

Some construction components made of carbon steels intended for outdoor use are

zinc-dipped or zinc-plated. Zinc protects these parts from the effects of atmospheric

corrosion. Assess what characteristics must the surface meet before applying the

coatings, and discuss how the coatings affect the recycling method of metal

construction components.

Comment on the construction design of the terminals shown in Fig. 1.2.1, the

suitability of the used materials and surface treatments. Try to suggest another solution

and the corresponding material so that it meets the requirements of the environment

specified by you.

Many components or parts from thin steel sheets are replaced by plastics. Give

examples and benefits of such replacements.

Some car manufacturers are considering substituting steel sheets used for production

of car bodywork with aluminium alloys. What problems can such a step reveal?

What are the advantages and disadvantages of composite materials?

Discuss the differences between the individual groups of construction materials?

What materials are used to produce food packaging and what conditions must they

meet?

Discuss the properties of wood and plywood which will be made of the same material.

Why does a heated glass break when exposed to sudden supercooling? How could the

probability of fracture be reduced in this case? What is the character of the glass

fracture surface?

2. The processes of a fracture breach

Study time 25 h

Objective

After studying this chapter, the readers should be able to:

Describe the most important factors affecting the process of fracture

breach.

Characterize the basic methods of breach stress.

Explain the size and shape of plastic zone at breach root.

Explication

One of the most important factors influencing the processes of the changes of the structure

of the constructional materials during their technical applications is the acting of the stress-

deformational field. This can be caused in the body, either by external forces, but it is also

necessary to look for its essence in its own, inner force interaction of the basic structure

components, caused especially by their non homogeneity, be it in the size, or in their spatial

setting. Other important factor influencing the stress-deformational behaviour of the materials

is the shape of the body. The surface, but also inner defects, dents, but especially sharp

breaches significantly divide stress-deformational field, the stress concentrates in their

environment, it causes strong plastic deformation, or localised breach damage of the material

and further spreading of the long breach. Dissipation of the deformational energy and gradual

relaxation of the stress happen during this process. The creation of the plastic zone in the

surrounding of the root of the breach, but also further processes of firming are significantly

influenced by the micro structure of the material and they have a decisive role during the

forming of the fractional instability, where the spreading of the breach is unstoppable. The

knowledge of the mechanisms of localised damage in the area of the intensive stress the

surrounding of the root of the breach, is a useful guide during the design and the optimizing of

the technological conditions of the production and the processing of the material. It is

necessary to evaluate the fracture of the body as a sequence of processes of damaging of the

structure as the result of inhomogeneity of the plastic deformation, which leads to the creation

of two new free surfaces. The fraction behaviour of the constructional materials has a static

character related to the localised damage. The methods of evaluation of the probability of the

creation of the fraction instability form inhomogeneity of stress-deformational field around

the concentrate of the stress, static division of the micro structural parameters and from the

knowledge of the micro mechanisms of the initiation of the damage, are the resources for the

prediction of the fractional characteristics of the materials, and are an important base for the

form design of the constructional parts. The dependence among the form of the constructional

part, the way of its stress and the characteristics of the micro structure of the materials, from

which these parts are produced, is determining for the objective evaluation of the safety and

operational reliability.

The stress in the cut is not homogeneous during the force stress of the constructional parts,

which have often a difficult form. Localized stress max nom is, in comparison with

nominal value of the middle value of the stress nom higher, in the area of the form

discontinuities, constructional dents or inner structural inhomogeneities of the material. An

example of such concentrator of stress can be a screw joint. Stress analysis of the screw in

the screw thread part is presented in the fig. 2. Dark areas are the places with the maximum

pressure stress; light areas are stressed more during drawing. As we can see, the nominal

stress in the middle part of the body decreases in the direction from the head of the screw to

the bottom. The calculations of the concentration of the stress are usually very difficult and it

is necessary to use numerical methods of final elements. The offer of the software is broad.

ANSYS, COSMOS, ABACUS and others belong among the most used software. Analytical

methods were used for the calculations of geometrically simple concentrators in the past. An

estimative evaluation of the coefficient of the concentration of the stress was usually

sufficient. It is defined easily as a share of maximum max and nominal nom stress,

nom

max

(1)

One of very useful practical examples is the knowledge of the division of the stress in the

area around the defect of elliptic form in the desk stressed by uniaxial drawing (fig. 3). The

coefficient of the concentration of the stress is in this case,

.21

c

(2)

its value is the higher and the longer the defect and the higher its sharpness is 1/. For the

limit case of the round defect, where the coefficient of stress is = 3 and maximal value of

stress is max = 3nom. The sharpest defect, on the other hand, is the breach c of the

semi-diameter of the sharpness , which gets nearer to the interatomic distance a0, a0.

screwhead

Fig. 2 The localisation of the drawing and pressing stress of the screw shank (adjusted according to

Němec, J., Puchner, O.: Tvarová pevnost kovových těles, SNTL Praha, 1971., Form solidity of metal

bodies – translated from Czech)

The critical moment, when the breach starts to spread from the most stressed root of the

defect, happens, when the maximum stress max exceeds the fracture stress f. We obtain the

ideal crystal if f is equal to the ideal solidity 2/100 )/( aEf , where E is a module of

flexibility and 0 is the surface energy (the energy necessary for the creation of a unitary area

of the free surface in the units Jm-2

). After simple approximation of equation (2) for a0 is

0nommax /2 ac and with the comparison with the ideal solidity the nominal stress

necessary for the spreading of the breach is,

.4

0nom

c

EF

(3)

There are many punctual, linear, but surface breakdowns in the setting of atoms in

technically used semi-crystalline materials, such as metals and technical ceramics.

Fig. 3 The concentration of the stress in the near of the elliptical defect in the desk stressed with uniaxial

drawing.

This is the main cause why the dislocations, surface defects and the borders of the grains

significantly decrease the stress needed for the spreading of the breach. The concentration of

the stress in the near of the root of breach becomes the source of simple slip motion of the

crystalline area during the creation of the dislocations by metals, especially at higher

temperatures. The root of the breach becomes duller, sometimes very broad plastic zone is

created in its area and the stress is much lower than if a direct fissure along crystal flat would

happen. The plastic zone can be so large, by large defects in the metal constructional parts

that it interferes into the cut of the body, also by nominal stress, which is significantly lower

than the limit of the shear y.

For example, in the area near a round opening in a desk, which has the measures

comparable with the size of the opening and is stressed with uniaxial drawing, a nominal

stress nom = y/3 is sufficient for the creation of the plastic deformations. The maximum

stress in the near of the opening is, as we can see from the equation (2), for = c, max = y..

The breach can be generally stressed in the body in three basic ways (fig. 4) and in the

dependence to what way it happens, the components of stress will change in the direction of

axes x1, x2. For the first, drawing mode of stressing (fig. 4) in the extension of elastic

reversible deformations the components of the stress will have this form:

,2

3cos

2cos

2sin

2),(11

r

Kr I (4a)

,2

3sin

2sin1

2cos

2),(22

r

Kr I (4b)

,2

3cos

2cos

2sin

2),(12

r

Kr I (4c)

where cKI

is a factor of intensity of stress dependent on an applied, nominal stress

and on the size of the breach c, and r, ϑ are the coordinates of the polar system of the

coordinates with the beginning in the root of the breach.

Fig. 4 The basic ways of straining of the breach, drawing mode I (a), shear mode II (b), cut mode III (c).

Parts of the stress in shear mode of stress (fig. 4b) have similar form and the factor of

intensity of the stress is labelled as KII. The factor of intensity of stress KIII is by cut mode of

stress (fig. 4c). The parts of stress of any chosen orientation of stressed breach can be

calculated by the linear combination, the composition of these three basic modes.

In metals where, by relatively low stress, is the plastic zone created around the root of the

breach, the stress field has an elasto-plastic character and the parts of the stress have modified

form. The comparison of the first parts of the stress 11(r,θ) for the elastic (equation (4a)) and

elasto-plastic solutions is presented in dimensionless coordinates 22 / Iy Kr and y /11 for the

coefficient of the deformational hardening n = 0.2 in fig. 5. It is necessary to use numerical

methods for the calculations of the stress field at larger expansion of the plastic zone in the

root of the breach that is by higher values of the nominal stress.

Fig. 5 The process of the drawing part of the elastic and elastoplastic field of stress in the area around

The size of the plastic zone rp and its form depend on the state of the stress of the body.

The first evaluation of the process of the elasto-plastic dividing line rp(θ) in the near of the

root of the breach, which length is in comparison with the dimensions of the desk

insignificant, can be obtained from Von Misses’ criteria of the plastic deformation for the

parts of the main stress 1 = 11, 2 = 22 (equation (4a), (4b)) and 3 = 0 for plane stress (PS)

and )2/cos(2/2)( 213 rKI for plane deformation (PD). The solution of this task

for both basic stress deformational states is graphically expressed on the fig. 6. During a gross

evaluation of the size of the plastic zone, it is sufficient to consider its size for = 0 and for

the conditions of the plane stress is then,

(5)

Fig. 6 The form and size of the plastic zone near the root of the breach stressed in the conditions of plane deformation

(PD) and plane stress (PS).

The plastic zone, as it can be seen in the fig. 6, is smaller for the conditions of the plane

deformation and it is only about )6( 22yIK . Even when the size and the form of the plastic

zone in metals are always a little influenced by the deformational hardening, this solution is

sufficiently accurate for technical applications. Because the state of the stress changes

significantly throughout the thickness of the body and conditions for the plane deformation

are not preserved on the surface, the plastic zone near the surface is larger than on the inside

of the body. This has the effects on the stress-deformational behaviour of the material during

the spreading of the breach.

Summary of terms

After reading this chapter, the reader should understand the following terms:

Describe the most important factors influencing the processes of structural changes.

Stress concentrators.

Construction dents.

Localized stress.

Fracture stress.

Surface energy.

Roots of breach.

Plastic zone at the root of breach.

The basic modes of breach stress

Questions

Calculate the critical carbide film thickness at grain boundaries of hyper-eutectoid steel

which leads to the initiation of micro-crack when the stress the steel is exposed to is

σ = 1000 MPa. The steel surface energy is 14 Jm-2

and the modulus of elasticity is

E = 210 GPa.

Calculate the critical deformation εn required to cavity nucleation on spherical inclusion

in steel with ferrite-pearlite structure, when the surface energy of inclusion decohesion is

6 Jm-2

, the inclusion modulus of elasticity is E* = 270 GPa and its size is 2r = 10 μm.

The composite is made of 40% of fibres with the diameter of 100 µm and the strength of

3 GPa and a matrix with the strength of 80 MPa. The interphase boundary strength of the

fibre and matrix is τm = 60 MPa. What is the strength of the composite when the fibres

have the length of a) 100 mm, b) 2 mm, and are kept in a matrix in the direction of the

applied stress.

What is the local cleavage strength value of ferrite-pearlite steel with a grain size of

d = 30 μm, when the surface energy for the formation of micro-cracks is 14 Jm-2

and the

Hall-Petch shear constant is kys = 0.3 MPa m

-1/2.

Practical example, Example to solve

A fracture blade failure may appear during the operation of a steam turbine. The fragments

can move at speeds of up to 600 m/s. Although the probability of a blade fracture is very low,

the consequences can be very dangerous. That is why protective guards are built around

turbines, in particular in nuclear power plants, which are designed to capture the fragments.

The guard design must be based on a numerical simulation of the blade fragment interaction

with an obstacle. This is due to the fact that the destruction of the blades may produce

fragments of different shapes, different sizes and hence weight, which move along various

curves and hit the guard at different angles and at different speeds. This variability of

degradation process characteristics is impossible to examine experimentally.

A reliable numerical simulation requires you to determine a credible description of the

material behaviour of both the blade and the protective guard and to suggest the damage

criteria at selected stress conditions. The selection of a deformation material behaviour model

depends on the type of task to be solved, and it is not quite possible to choose the material

behaviour model solely on the basis of theoretical considerations. The following program has

been designed to acquire data of reliable numerical simulation of the aforementioned

interaction:

Determination of material properties of the blade and guards under shock stress.

Design and execution of an experiment when a flat plate is exposed to impacts of

turbine blades and fragments of this blade. These experiments will be used to evaluate

especially the residual blade speed and its fragments, i.e. the speed after plate

penetration.

Numerical simulation of the designed experiment using the description of the

behaviour of the material acquired in the first point. The objective is the parameter

optimization of the designed constitutive equation and the determination of the

conditions for the occurrence of material damage.

The results of this project have shown that the suggested procedure has led to designing a

reliable numerical simulation of the turbine blade interaction with a flat plate. The model

simulation result is graphically shown in the picture.

Sample of blade fragment penetration of the plate in time of 0.0012.

(The model was presented with a kind permission of the author, Prof. Ing. Jaroslav Buchar, DrSc. from the

Mendel Agricultural and Forestry University in Brno.)

3. Basic characteristics of the fatigue damage

4. Study time 15 h

Objective After studying this chapter, the readers should be able to:

Describe the most important factors influencing the process of fatigue

damage.

Characterize the basic factors affecting the rate of fatigue breach

propagation.

Describe the cyclic deformation curve.

Explication

The absolute majorities of the constructional parts of machines and devices are subjected

to the effects of the time changing parts of the stress during their technical operating. Regular,

cyclical, also irregular, stochastic process of the stress (fig.7) causes a creation of a plastic

deformation, initiation of fatigue breaches, their spreading and a fracture of the body in the

narrowly localised, most stressed volume of the material.

Fig.7 Regular cyclical (a) and irregular stochastic (b)

process of the stress in dependence on time.

Fig. 8 Macroscopic picture of the fatigue

breach of a rotor, which merges into the final

quick break. The initiation of the fatigue breach

is labelled by an arrow.

Highly stressed surface layers of the constructional parts and their inequalities caused by a

mechanical process, corrosion or imperfection of welded joints, are the most common places

of initiation of the fatigue breaches. The initiation and the growth of the fatigue breaches are

influenced by the level of stress, quality of process and also by other parameters,

microstructures, inner tension, temperature or by the effects of the influences of the corrosion

environment. A picture of the fatigue breach of broken body of a rotor, where the fatigue

breach of elliptic form turns into the final quick break, is shown as an example on the fig. 8.

The constructional solutions, technology of production especially surface modification of the

constructional part are very important for the securing of its desired durability, because the

division of the stress during the stress of the constructional part strongly depends on its form.

Localised plastic deformation, which was created as a result of time changing part of the

stress, strongly influences further stress-deformational behaviour of the constructional parts

during operation. The changes of dislocation structure during the creation of the plastic

deformation have their results in the hardening or in the softening of the material, and they

even can significantly divide the field of the stress in the body. The response of the body to

the cyclic stress depends on the way of its straining. This is determined either by the limit

value of the stress, lower d and upper h stress of the straining cycle (fig. 9 c, d) or by the

limit value of the deformation, lower deformation d and upper deformation h (fig. 9 a, b).

The character of the cyclical straining can be expressed by the coefficient of the

changeability of the cycle by a defined ratio,

.d

hR

(6)

The amplitude of stress and amplitude of deformation are defined analogically from the

upper and lower value of the stress and deformation,

dhΔ a dhΔ (7)

Amplitude of stress and amplitude of deformation,

)(2

1dha a )(

2

1dha (8)

and medium stress and medium deformation,

)(2

1dhm a ).(

2

1dhm (9)

When R = 1, from the definition of the coefficient of changeability of the cycle h = d and

the material is stressed statically, when d = –h is R = –1 and the material is stressed by

alternating straining. The lower stress can be up to d = 0, R = 0 by the pulsar straining of the

walls of the pressure systems and the straining is called passing. Practically, the coefficient of

the changeability of the cycle changes in broader interval of values and in the limit case, when

the drawing part of the stress cycle h → 0, is R → – ∞ .Acting of the time changeable part of

the stress causes the deformation in the constructional part, which, similar to the stress during

the straining, changes. Basically two ways of straining exist in the dependence to the

deformation caused by the cyclic part of the stress. Soft cycle, by which the amplitude of

stress a is kept on a constant level. Hard cycle, when the amplitude of deformation a (fig. 9)

is kept on a constant level. Time process of the deformational response is monitored during

the control of the cyclic straining by the stress characteristics of the soft cycle. And the time

process of the stress response of the material is evaluated during the control of the cycling in

the deformational characteristics of the hard cycle.

The dependence between the cyclical part of the stress and deformation, is described by the

cyclic stress deformational characteristics.

Fig. 9 The response of the material to the cyclic straining: (a) cyclic hardening controlled by the deformation,

(b) cyclic softening controlled by the deformation, (c) cyclic hardening controlled by the stress,

(d) cyclic softening controlled by the stress.

Generally, during the examination of the response of the material on the cyclic straining,

be it in stress or deformational mode, these cases can happen (fig. 9). The material can either

cyclically harden, and then the amplitude of the stress by the constant amplitude of

deformation grows (fig. 9a), or cyclically soften and then the amplitude of stress by constant

amplitude of deformation falls (fig. 9b). If the cyclic stress is controlled by the stress part, the

material cyclically hardens, when the deformation with the growing number of cycles falls

(fig. 9c). The material cyclically softens, when the deformation with the growing number of

cycles grows (fig. 9d).

Often, in dependence to the fact, which of the both processes, of cyclical hardening or

softening predominates, the amplitude of the deformation may grow in the first phases of

straining by the constant amplitude of stress and the material cyclically softens, when, in the

second phase it falls and the material cyclically hardens.

The cyclical curve of hardening (fig. 10) is defined as a geometrical place of the tops of

stabilized hysteretic loops, that is the amplitudes of stress a and amplitudes of the

deformation a, can be similarly to the quasi-static straining represented by the relation,

,´

1

naa

aKE

(10)

where n' is the cyclic coefficient of deformational hardening and K' is a constant of the

material. A growth of amplitude of the stress a happens during the cyclic hardening

controlled by the deformation (fig. 9a) and by constant amplitude of stress (fig. 9c) there

comes to the decrease of the amplitude of the deformation a, cyclic curve of hardening of

stabilised BH loops is situated above the quasi-static stress-deformational characteristics. In

comparison to the coefficient of the deformational hardening of the material n, cyclic

coefficient of the deformational hardening n' is lower by metals and it lies in a narrower area

of values, usually from 0.05 to 0.25.

At sufficient value of the amplitude of stress a there comes to gradual cumulation of the

damage of the material during the cyclic straining, which leads eventually to the fracture of

the constructional part. Growing value of the amplitude of stress a, as well as the growth of

the upper stress h the durability given by the number of the cycles in the fraction Nf

shortens.

The curve of the durability, or also Wöhler’s curve, which is stated in fig. 11, for the

typical three values of the coefficient of the changeability of the cycle R, is falling function of

the amplitude of the stress. The curve of durability is usually divided into five basic areas:

a) the area of quasi-static fraction, b) the area of cyclic flowing, c) the area of low cycle

fatigue, d) the area of high cycle fatigue, e) the area of safe straining.

Fig. 10 Quasi-static and cyclic curve of hardening for C-Mn steel with denotation of upper parts of

stabilised loops (adapted according to Lefebvre, D., Ellyin, F.: Int. J. Fatigue 6, 1984, 9). (Translation

of the picture: cyklická – cyclic, kvazistatická – quasi-static, stabilizované hysterézní smyčky –

stabilized BH loops)

Fig. 11 The scheme of Wöhler’s curve of durability and the definition of the basic areas.

The area of acute decrease of the limit value of the upper stress h is labelled as the area of

timed fatigue hardness and the area of safe stressing is labelled as the area of chronic fatigue

hardness. The machine part is broken either statically in the first semi-cycle in the area of the

quasi-static fracture and the limit value of the upper stress is equal between the hardness of

the material Rm or it is broken after a few tens of cycles, when h < Rm. A force function is

often used for the description of the limit value of the upper stress h on the number of the

cycles into the fracture Nf in the area of the timed fatigue hardness.

It has the form of,

,)2(* bfhfh N (11)

where *hf is coefficient of the fatigue hardness, which is given by extrapolation of the curve

of durability on the first semi-cycle of stress 2Nf = 1 and b is coefficient of the fatigue

durability. The limit value of the stress, under which the failure of the material does not

happen even after 107 cycles, the limit of the fatigue hc depends, besides the straining, also

on the form of the constructional part and on the character of the surface layers.

The level of the plastic deformation is also the parameter controlling the fatigue failure of

the material; for the evaluation of the durability we usually use, besides the Wöhler’s curve,

especially in the area of low cycle fatigue, the dependence of the number of the cycles on the

amplitude of the plastic deformation ap. This dependence called Manson-Coffin dependence

has similar form to the equation (11),

,)2(* cffap N (12)

where ɛ*f is the coefficient of the fatigue dilatability, which is given by the extrapolation of

the amplitude of the plastic deformation on the first semi-cycle of straining (2Nf = 1) and is

equal dependent on the material 0.35 ɛf - ɛf , where ɛf is the fracture deformation during the

dilation test and c is the coefficient of the fatigue durability. The amplitude of the plastic

deformation ɛap is stated, on the fig. 12, as the function of the cycle into the fracture, together

with the amplitude of the plastic deformation ɛap as the function of the number of the cycles

into the fracture is stated together with the amplitude of the plastic deformation ɛae for C-Mn

steel. The number of the cycles, by which the elastic part of the amplitude of the deformation

is equal to the plastic part, is sometimes used as the criteria for the distinction of the areas of

low cycle and high cycle fatigue of the material.

Basic characteristics of the stabilised stress-deformational behaviour of the material during

the cyclic straining are the base for the engineering design of the constructional parts. Other

factors play an important role during the evaluation of the durability of the real constructions

Fig. 12 The elastic, plastic and total amplitude of the deformation of C-Mn steel dependent

on the number of the cycles into the fraction and Manson-Coffin approximation

(according to Lefebvre, D., Ellyin, F.: Int. J. Fatigue 6, 1984, 9).

stressed by time changeable part of the stress; there belong the way of straining and the state

of the stress of the constructional parts, the quality of their surface layers or the local

concentrators of stress. All these factors do not only influence significantly the final stages of

the spreading of the fatigue failure, but its initiation as well.

The changes of the current stress, changing of tractive and pressure part during the

straining and unloading of the body, open the root of the initiated breach and close it again, so

the breach starts to spread. The fracture areas come closer together after unloading of the

breach during the decrease of the stress, however the new surface created during the tractive

phase of the cycle is not fully reversible by the effecting of the reverse plastic deformation

and fatigue corrugations form in the front of the breach, these are labelled as striations. An

example of such fracture area of carbon pod eutectoid steel is on the fig. 13. The area of the

remaining fracture, which is created by accordingly long fatigue breach as the result of the

loss of the bearing capacity of the constructional part, has usually trans-crystal fragile

character.

Fig. 13 Characteristic striations on the fracture area of the fatigue fracture of austenitic steel AISI 304 L

(with a consent from the author Prof. Ing. Ivan Nedbal, CSc., KMAT FJFI ČVUT Praha).

The quickness of the spreading of the fatigue breaches is influenced by many factors

such as, amplitude of the applied stress a and the way of straining given by the coefficient of

the changeability of the cycle R, the state of straining, but mostly by the stage of spreading, in

which the breach is at the given time, that means its length c. Because the length of the breach

grows during the straining, the amplitude of the factor of the intensity of the stress grows as

well in its front .cΔΔK The fatigue breaches are initiated usually as the consequence of

the plastic deformation on the surface of the constructional parts. With the growing number of

cycles, short fatigue breaches grow, spread into deep and then long major breach is formed,

which leads into the final break of the constructional part. While the spreading of the long

major fatigue breach is possible above the limit value of the amplitude of the factor of the

intensity of stress ΔKth, expansion of short fatigue breaches can happen also below the value

ΔKth (fig. 14).

Originally postulated by Paris, the linear dependence of logarithm of speed of spreading of

fatigue breach on the logarithm of the amplitude of the factor of the intensity of stress log ΔK

was experimentally revised many times and not only in metal materials, but also in technical

ceramics. Its analytical form is as follows,

, d

d KCΔN

c (13)

where C and β are parameters of material.

Fig. 14 The speed of the growth of the fatigue breach of carbon steel as the function of the amplitude of the factor of

intensity of the stress and the coefficient of the changeability of the cycle in highly solid martensitic steel (adapted

according to Kujawski, D., Ellyin, F.: Engng. Fract. Mech. 28, 1987, 367). (Translation of the picture: oblast krátkých

trhlin-area of short breaches; oblast dlouhých trhlin-area of long breaches)

Summary of terms

After reading this chapter, the reader should understand the following terms:

Stress amplitude and defomration amplitude.

Amplitude of stress, medium stress, amplitude of deformation, cycle variability

coefficient.

Cyclical hardening curve.

Cyclical coefficient of deformation hardening

Durability given by the number of cycles in fracture.

Wöhler’s curve.

Five basic areas of durability curve.

Manson-Coffin approximation.

Criterion used to distinguish the areas of high cycle fatique and low cycle fatique of

material.

Striation

Threshold amplitude of stress intensity factor.

Questions

The cycle variability during cyclic machine part stress is R = –1/3. What is the upper

stress when the intermediate stress m = 50 MPa

Estimate the fatigue limit c of Cr steel 14 240, whose static strength is Rm = 780 MPa.

In 1CrMoV steel used for the production of energy equipment rotors, the rate of fatigue

breach propagation is given by the relation:

.107.7d

d 312IΔK

N

c

Calculate minimum and maximum rate of fatigue breach propagation when the amplitude

threshold of stress intensity factor is ΔKth = 5 MPam1/2

and the fracture toughness of this

steel is 115 MPam1/2

.

A component of steel energy equipment with the fracture toughness of Kc = 54 MPam1/2

has been subjected to non-destructive ultrasonic testing, and it has been found that it

contains defects reaching the size of up to 2a = 0.2 mm. Laboratory tests have shown that

the rate of breach propagation under the influence of cyclic stress follows the Paris' law

with the constants of C = 4·10–13

MPa–4

m–1

and = 4. Calculate the number of cycles to

failure when the acting stress amplitude in case of transient stress is = 180 MPa.

4 . Creep

Study time 20h

Objective After studying this chapter, the readers should be able to:

Interpret the basis of creep damage

Describe the basic types of creep

Describe the basic mechanisms of material failure appearing during creep

damage.

Explication

The long term stressing of the constructional materials at higher temperatures, sometimes

also during the stress which is lower than the limit of the shear, creates time related plastic

deformation called creep. The character of the dependence of the creep deformation on time

is influenced by the chemical composition and the microstructure of the material, the

temperature and active stress. These parameters are decisive for a micro mechanism, which

causes the creep plastic deformation and they, to a certain point, influence breach damage of

the material during creep and the character of the fracture process.

Basic creep characteristics, the dependence of the creep deformation on time, change

depending on the conditions, especially on the temperature T and applied stress, which decide

about the dominant creep mechanism. Three basic typical relations of the creep deformation

on time are presented in the fig. 15, and they are always valid for the constant temperature T

and applied stress.

The dependence of deformation on time during low temperature creep, is usually described

by the logarithmic function,

0)1ln()( tt ll , (14)

where l and l are constants and 0 is an immediate deformation created immediately after

the stress, that is in time t = 0. It is clear, from the fig. 15, where this characteristic is stated

that after the initial quick growth, the deformation stabilise, and in some cases it does not

have to change even after a long time.

The speed of the deformation decreases during the low temperature creep from the initial

value l αl after the sufficient time t up to zero (fig. 16). The low temperature creep

deformation, which behaves in accordance to the logarithmic law (equation (14)), can bee

seen in Cu, Al at temperatures lower than 200 K, in some steels with HCP crosshatch, but

also in glass materials and elastomers.

The dependence of the deformation on time during high temperature dislocation creep has

these three characteristic areas (fig. 15). During the first stage, sometimes called primary or

transitional creep, the creep deformation grows, similarly to the low temperature creep, and

to the decrease of the speed of the deformation onto the so called minimum speed of creep

min (fig. 16). The time dependence of the creep deformation of the primary creep, is usually

directed by the Andrade’s creep law in the form,

Fig. 15 The typical relations of the creep

deformation on time, during high

temperature creep is the marked area 1 –

primary creep, 2 – secondary creep and 3

– tertiary creep. (Translation of the figure:

vysoká T – high T, vysokoteplotní

dislokační creep – high temperature

dislocation creep, logaritmický creep –

logarithmic creep.)

Fig. 16 The typical relations of the speed

of the creep deformation on time.

0')( m

att , = constant, T = constant, (15)

where a is a constant, 0 is an immediate deformation, which happens in the material

immediately after the stress and m´ is an exponent, and its value depends on the stress-

deformational behaviour of the material. For the ideal elastic materials are m’ = 0,

deformation (t) = constant, do not depend on time and are equal to the immediate initial

deformation under the stress .

The second stage of the high temperature creep, which is also called secondary or

stationary creep, has an approximate equilibrium between the deformational hardening and

restoration and the dependence of the deformation usually responds to the relation,

0)( tt s , = constant, T = constant, (16)

where s is the speed of the stationary creep.

In the third stage of the high temperature creep, tertiary creep, the deformation is usually

the power of the function of time, ´́ mt , where m´´ > 1 and usually m´´ = 3, and that is

why the dependence of the creep deformation on time, is during the high temperature creep,

when we considerate all three stages given by the relation,

03/13)( tttt sa

, = constants, T = constant, (17)

which was originally drafted by Graham and Walles (Graham, A., Walles, K.F.K.: J. Iron

Steel Inst. 1979, 1955, 105).

The character of the dependence of the deformation on time naturally changes with the

growing effects of the stress during creep stress of the material. While at low values of the

stress there is, during the high temperature creep fairly long stage of the secondary creep, with

growing stress this stage significantly shortens and at very high values of the stress, but also at

accordingly high temperature, its total dematerialization can happen. The form of the creep

curve then comes nearer to the curve of dislocation creep, which happens at high stress and

high temperatures (fig. 15). The period of the fracture is much longer at low values of stress in

the comparison to the high stress, but the deformation of the fracture f is lower.

The speed of the high temperature creep has a similar influence as the growth of the stress,

especially at temperatures higher than 0.4 TM, which is the growth of the temperature. The

dependence of the speed of the creep with the temperature can be generally described by the

Arrhenius’ law,

RT

QT Cexp)( 0 , (18)

where QC is activation energy of the creep, R = 8.31∙10−3

JK−1

mol−1

is a universal gas

constant and 0 is a frequency factor. Activation energy of the creep is in the first accession

equal to the activation energy of the micro-mechanism of the creep (chapter 5.3.2) and

because the micro-mechanism of the creep depends on the temperature, the activation energy

of the creep is also a function of the temperature.

The diffusion creep is a prevailing mechanism of the creep at the low temperature and the

activation energy QC is low. The growth of the activation energy of the creep slows down

with the growing temperature and the creep is controlled by the combination of mechanisms

of dislocation and diffusion creep. The directing mechanism of the creep is the dislocation

creep in the third area where the activation energy of the creep is comparable with the

activation energy of the diffusion of vacancies QD, The temperature, at which the activation

energy of the creep reaches the value QD, the growing function of the speed is the

deformation. It is obvious from the equation (18) that the dependence of ln on 1/T is linear

and the activation energy of the creep is equal to R multiple of the tangent of this dependence.

The character of the dependence of the deformation on time changes during the high

temperature creep with the growing temperature, similarly to the change of the active stress.

The stage of the secondary creep shortens and the fracture deformation f grows with the

growing temperature, as it can be seen in the fig. 17, where the creep characteristics of

aluminium for three different temperatures are shown.

This relation can be used during the evaluation of the influence of both main factors

influencing the speed of the stationary creep, temperature and active stress,

RT

QfT C

s exp)(),(0

, (19)

where f() is a function of the acting stress, and its form depends on the fact, if the interval is

of low, medium or high stress. resp. (5.3.11). The speed of the stationary creep can be

approximated in most cases of the technical materials with the easiest form of the equation

(19), that means for f() = constant n´

.

Summary of terms

After reading this chapter, the reader should understand the following terms:

The principle of creep deformation.

Arrhenius’ law, Andrade’s law.

Speed of creep.

Stationary, transitional, tertiary and dislocation creep.

The activation energy of creep.

Fig. 17 The dependence of the deformation on time

and temperature during creep of pure aluminium

(adapted according to Dorn, J.E.: Creep and

Fracture of Metals at High Temperature, Proc. NPL

Symposium, 1956).

Questions

Calculate how many times will the creep rate of pure aluminium increase when we apply

the stress of 21 Mpa, when the temperature increases from 424 K to 531 K and the

activation energy of creep has the value of Q = 142 kJmol−1

and R = 8.314 Jmol−1

K−1

.

The creep rate of pure aluminium at the stress of 21 MPa and temperature of 531 K is

5∙10−4

s−1

. What is the time to fracture when the fracture deformation under these

conditions has the value of εf = 0.8?

Assuming that creep at constant temperature and under stress follows the law of ε = δtm,

determine the time necessary to achieve 3% deformation of heat resisting steel, when the

time to 1% deformation of this steel is t1 = 20 000 h and parameter m = 2.5.

5. Corrosion of metal materials

Study time15 h

Objective After studying this chapter, the readers should be able to:

Understand the principle of corrosion damage

Explain the influence of corrosion on the mechanical properties of

material

Interpret the basic parameters of corrosion damage

Explication

The constructions of the machines and devices are often exposed to the chemical effects of

surrounding gaseous or liquid environment during their operation. Chemical interaction

between the surrounding environment and the metal parts significantly devaluates, not only

their surfaces, but also their inner structure of the material. The corrosion damage, chemical

effects on the material, worsens its strength properties and plastic characteristics and it leads,

in many cases, into a complete loss of the function of the construction, into the creation of the

fracture or to its corrosion through and through. The decreasing of the utility characteristics of

the material as an effect of the corrosion is expressed also by a worse transfer of the heat,

worsening of esthetical characteristics, but also by the growth of the risk of pollution of the

environment, where corrosion happens, for example the contamination of water, soil, food,

body fluids etc. by corrosion products.

It is possible to distinguish the corrosion by the extent of the damage into a total corrosion,

which happens on the whole surface exposed to the corrosion environment equally and into a

local corrosion, or localized corrosion, which happen intensively only in some parts of the

exposed surface of the metal. The loss of thickness of the material, weakening of the wall of

the construction part or worsening of the fragile fraction characteristics of metals are the

results of the chemical reactions during the total corrosion.

The speed of the equal or total corrosion, which happens on the whole surface of the metal

with a comparable intensity, is most often expressed in units of a decrease of thickness of the

material in a time unit, for example in millimetres a year [mma−1

] and according to the type of

the corrosion system that means the combination of metals and environment, can increase

values in few degrees. For example the speed of the dilution of carbon steel in sulphuric acid

is 50−100 mma−1

, but the speed of the corrosion of the same material can reach only the range

from 1 to 50 ma−1

during atmospheric conditions. Because of the fact that the corrosion

cannot be totally suppressed in many cases, it was necessary to implement technically

acceptable limits of the speed of corrosion that means an allowed intensity of corrosion, at

which it is possible to expose the constructional part to the corrosion environment for a long

time without unacceptable changes of their utility characteristics or worsening of other

monitored parameters, the appearance of the surface, worsening of the transition of the heat

and the like.

Many corrosion systems with planned durability in the range up to 30 years have

technically acceptable corrosion speed lower than 0.1 mma−1

. Characteristic dimension of the

parts of the construction, for example the thickness of the wall, has to be increased, in this

case, for the estimated decrease of the period of the planned durability, so called corrosion

addition. In some constructions with higher durability, up to 100 years, the corrosion speed is

acceptable on the level of 1 to 10 ma−1

. In ferroconcrete mountings the average speed of the

corrosion of steel mounting is allowed only about 1 ma−1

. Dangerous cracks which are

created in the concrete happen at higher corrosion speeds with emerging products of

corrosion. Parts of the electro technical industry, where some metal or semiconductor parts

can put on the measures in the range from 10 nm to 100nm, the acceptable corrosion speeds

are much lower and the corrosion of 10% of the thickness of the copper layer on the

integrated circuit, which is a creation of one to few monomolecular layers of copper oxide on

the surface, can lead to a significant voltage losses and to a consequent breakdown of the

whole component.

Other aspect for the limiting of the maximum corrosion speed is the demand of the

smallest possible contamination of the environment from the products of the corrosion. For

example by body metal replacements, the releasing of soluble corrosion products of cations of

metals, even by the preserving of the functional characteristics of metal implant, lead to

unpleasant health complications.

The speed of the growth of the corrosion products onto the surface of metal is not the same

and depends especially on the conditions and mechanism of corrosive attack. However,

mostly the growth of stronger, especially oxidic layers follows the law,

,ktxm (20)

where k is constant, t is time, and m is exponent, which moves in the range from 1 to 3. For

the growth of strong oxidic layers at high temperatures the leading action of oxidation is the

diffusion of ions of metal with the layer of oxide of the thickness x and constant m 2. The

speed of the growth of thin oxidic layers is directed by other regularities.

Many metals, which show natural, thermo dynamic ability for the creation of the corrosion,

have large stability under certain conditions. It is caused by breaking of corrosion reaction

with the creation of the corrosion products, most often oxides on the surface of the corroded

metal. The surface of the metal passivates. Immunising layer on the surface of the metal has

usually the thicknesses below 10nm and protects the metal relatively well against other more

intensive progresses of corrosive attack. The creation of immunising layer is the main reason

of high corrosion endurance of the steels which are proof against the corrosion, aluminium

and titan and that is valid also in watery environments. Breaching of the immunising layer, for

example in a chemical way, by the effects of chlorides or by mechanical breaching, leads

usually to a major acceleration of the corrosion in the failure and localised corrosion damage

happens.

Other very important action, which conditions the process and influences the speed of

corrosion reactions, is the ability of the reduction of the environment or some of its parts.

Metals oxidise during the corrosion and its progress is possible only when, the reductive

reaction happens at the same speed on the corroding surface. If the speed of the reduction

reaction is slowed down by something, it is expressed in the speed of oxidizing reaction. For

example in exhausted gases it can be a limited access of the oxygen to the surface of the metal

through the layer of oxides or a slow input of matters to the surface of the metal in the

dilution.

Summary of terms

After reading this chapter, the reader should understand the following terms:

The principle of corrosion damage

The extent of corrosion

Corrosion speed, corrosion speed limits

Corrosion addition

Corrosion reaction

Passivation layer

Questions

A connecting T-piece of hot water distribution piping made of brass CuZn30 cracked and

began leaking after a certain period of use. On the basis of a visual survey, it was found

that there had been no corrosion. Consider all the options explaining why the T-piece was

damaged.

Various metals are commonly used to protect steel construction components, including

Zn, Pb, Sn, Al and Ni. Select those of these metals which do not show any basic material

corrosion, even if the coating is damaged, for example by mechanical scratching.

Austenitic stainless steels often corrode around welds in thermally affected zone. Try to

explain why this corrosion occurs. How can we prevent this type of corrosion?

Pure tin is often used for electronic connections of Cu contacts. Which of these two

metals is likely to be the anode?

Steel sheet with the surface area of 1 m2 is galvanized on both sides with the layer

thickness of x = 0.05 mm. The sheet is subjected to the effect of current density of

j = 0.02 Acm−2

in aqueous environment. Assuming that Zn dissolves evenly throughout

the entire sheet area, calculate the time necessary to reveal the steel surface.

6. Basic mechanisms of the wear and their characteristics

Study time 10 h

Objective After studying this chapter, the readers should be able to:

Understand the basic mechanisms of surfaces wear of two bodies.

Understand the processes in material which occur during the process of

wear.

Interpret the effects of frictional forces and force interactions of two

functional surfaces of bodies.

Explication

The changes of the conditions of acting of frictional forces and force interactions of two

functional surfaces of the bodies during their mutual tangential motion, which result in the

plastic deformation of the surface layers, localised concentration of stress and creation of the

micro breaches or to high heating of the surface and to its oxidation, lead to volume decrease

of material called depreciation. Unwanted changes of the geometrical, chemical, physical and

especially mechanical characteristics of the surface layers can cause, as the result of the

depreciation, especially at high pressure forces, the creation of micro-joints and to jamming

of functional surfaces. Excessive WEAR and often its inequality in the contact area becomes

one of the main reasons of the loss of a secure functioning of the constructional parts. The

WEAR caused during the tangential force interaction of the surfaces happens mostly in gear

wheels, transmission of the functional parts of bearings, contact areas of brake systems, knifes

and razors, but also in many parts of the construction machines and the means of transport.

The speed of the wear W [mm3/m] is contractually defined as a decrease of the volume of

the material on a unit of length of the slipping of the functional surface. The function of

WEAR for the given geometry of the bodies during tangential motion is the pressure force P,

relative speed of motion v, initial temperature T0 and thermal, mechanical and chemical

characteristics of both materials. Sometimes volume decrease of material Vw [mm3] also

called volume abrasion, is used for the evaluation of the depreciation. The mechanism of

WEAR changes, in relation to the stated parameters and in some cases the speed of the

WEAR W can be influenced by two or more mechanisms in a mutual interaction. It is

appropriate to consider the WEAR related to a unit of acting force, measurable speed of

WEAR or normalized speed of WEAR W~

defined by the coefficient of measureable speed of

WEAR and hardness of the material H for the evaluation of the relation of speed of WEAR W

on the acting force,

P

Ww [mm

3/Nm]; ,

~

0A

WHwW (21)

where A0 is a nominal area of the contact. Because normalized speed W~

is related to the unit

of the area, it is possible to use it also for the comparison of the WEAR of the bodies of

unequal sizes, which move at the different speeds. The mechanisms of WEAR strongly

depend on the conditions of the stress, on the character of the force contact of pair of

materials, on their characteristics and on lubrication mechanisms of contact surfaces, and so

the specific speed of WEAR is in very wide range of values from 10−15

− 10−1

mm3/Nm.

Sometimes even small changes of conditions can cause decisive change of the controlling

mechanism of depreciation.

Fig. 18 Typical dependencies of volume abrasion on the length of contact surfaces during adhesive

depreciation. (Translation of the figure: keramické materiály – ceramic materials, kovy – metals,

stacionarní opotřebení – stationary depreciation, zadření – jamming, stadium záběhu – stage of inrun,

Délka proběhu v kontaktu L – The length of the process in the contact L, Objemový otěr – volume

abrasion.)

One of important circumstances influencing the progress of the mechanisms of the WEAR

and the volume abrasion as well Vw is the time, during which, are the functional surfaces in

mutual, repeated force contact. Because for the constant speed of motion v the time derivation

of volume abrasion dVw/dt is equivalent derivation of the volume abrasion according to the

length of slipping of the functional surfaces, which is equal to the speed of WEAR W, it is

enough to evaluate the progress of the dependence of the WEAR on time, easily by the speed

of the WEAR W. The speed of the WEAR can be, in relation to the length of the contact of

two surfaces L, either constant, and then the volume abrasion Vw is a linear function of time

(fig. 18), or it has transitional character and after the initial fast growth, the WEAR in the

second stage gets into a stationary state with constant, low speed of WEAR W. Sometimes

there can be also the third stage with repeating extreme growth of speed W, which causes the

loss of the function of the contact. This type of the dependence of WEAR on time is often

seen by metals. Other type of time process of the WEAR is the transition of the speed of the

WEAR from the stationary state into the state of the progressive growth of speed. This

progress of WEAR is typical for ceramic materials. Different dependencies of roughness of

the functional surface on time relate to the stated three basic time progresses of depreciations

(fig. 18). The roughness of the surface is constant in the relation to time during linear progress

of the WEAR. Other two cases of the dependence of the roughness of the surface during the

WEAR on time is the initial growth followed by the stabilisation and decreasing of roughness,

which stabilises after a certain time. The last character of the dependence of the surface is

expressed during the mechanisms of polishing and finishing of the surface.

The WEAR can be studied from many views. It can be a way of a mutual motion of two

bodies, the character of the force contact of two functional surfaces, or dynamics of their

mutual interaction. The use of all these approaches is appropriate during the evaluation of the

functionality of machines and machine parts during tangential or rotational movement,

however it does not allow to estimate the process of the WEAR dependent on time during

heavy stressing, the meaning of each factor, which influence the WEAR and especially the

process of the mechanisms, which cause the WEAR under different conditions. The basic

mechanisms of the WEAR of the surface of two bodies, during their mutual tangential

movement are adhesive depreciation, abrasion, fatigue WEAR and corrosive depreciation.

The creation of the adhesive WEAR is the result of the effects of strong, adhesive forces

during plastic contact of the surfaces. Breaches which are under the surface, which spread

under the combined influence of pull and shear stressing, cause a tearing of the particles of the

material from the surface and volume abrasion. Cutting and striation of the surface, called

abrasion, happens during the plastic deformation of the surface of softer material, which is

intruded by harder particles.

The result of this intensive plastic deformation, sometimes accompanied by the hardening

of the surface layers, is the creation of often sharp edged particles of the material and volume

decrease. While the adhesive and abrasive WEAR can happen without the plastic deformation

of surface layers, fatigue and corrosive depreciation happens also by elastic stressing of the

surface layers. The fatigue WEAR is induced by a repetitive force contact of two bodies,

when mechanisms of localised plastic deformation in the near of the surface come into the

emergence of the surface breaches and to husking of the particles of the material. When the

tangential movement of two bodies loaded by the pressure forces happens in the corrosive

environment and layers of corrosive products are created under the influence of chemical or

electro-chemical reactions, the processes of WEAR accelerate and they are generally labelled

as corrosive depreciation. The surfaces are sometimes depreciated as a result of the effects of

high abrasive forces and extreme increase of the temperature of surface layers, often

accompanied with the creation of the phase transformations, smelting or initiation of the

surface breaches. Depreciation, which is created as the result of these processes, is sometimes

labelled as the thermal depreciation.

Summary of terms

After reading this chapter, the reader should understand the following terms:

Adhesive wear, abrasion, fatigue wear and corrosion wear.

Measurable speed of wear, normalized speed of wear

Thermal wear

Questions

What measures to minimize abrasive wear of functional surfaces would you suggest if the

hardness of the abrasive were low or high. How would these measures change when the

angle of abrasive particles impact increases from 5 ° to 45 °.

Describe the process occurring during fretting and how the friction coefficient changes in

relation to the number of cycles during the oscillation in your opinion.

Explain the difference in the dependence of erosive wear on the angle of impact of SiC

erosive particles on the surface of a sheet made of carbon steel and stoneware. What are

the main factors influencing this difference?

What conditions must be met by a material resistant to cavitation wear.

Calculate the adhesive wear speed of a nylon skid moving on austenitic steel surface at

the speed of υ = 1.5 ms­2

stressed by force N = 550 N. The shear stress in the nylon

surface layers is τ = 70 MPa and the coefficient of friction μ = 0.66. The Archard constant

of this pair of materials is kA = 1·10­8

. Take into account the speed of the adhesive

measure to estimate the thickness loss of the skids during one day of operation at the

specified conditions. Comment on the result.

7. The conclusion

Study time Not specified – depends on the understanding of the contents of the

individual chapters.

Objective The objective of this chapter is to provide a complex summary of

previous chapters

Explication

Higher level of reliability and safety of the constructional parts, but also the demands for a

longer durability of the products, are the basic reasons, why new constructional materials are

produced, or why there are changes of materials in new constructional solutions of products.

But even new materials with better utility characteristics do not stay unchanged in their

behaviour during the time of their technical application. Long time, often time changeable

activity of forces, higher temperatures and chemical actions of surrounding environment

cause the WEAR of the material, and with that comes lower reliability of the constructional

parts. Often very complicated changes of the structure of the constructional materials, which

are caused by these WEAR processes, lead to chronic deformations, to the creation of

breaches or to an excessive depreciation. Because most of these WEAR processes have a

character of long time, it is possible to identify them in time with effective diagnostic

methods, and prevent sometimes even large damages during the failure of the constructions. It

is not easy to state if the construction is in critical state, which is also called limit state of the

construction. It requires much experience, not only from the area of the construction of the

device, but also the knowledge of the WEAR processes and about the constructional

parameters and their changes in the relation to changes of the mechanical characteristics. The

knowledge of the mutual relation between localised damage of micro-structure and limit state

of the construction is one of the key conditions for the correct estimation of its safety and

residual durability.

The development of new constructional materials, which would guarantee a higher

resistance against the WEAR processes, not only includes the design of their structure, which

means the requirements for the micro structurure characteristics in the relation to the

mechanical characteristics. The relation of mechanical characteristics, chemical constitution

of material and technology of its production and the processing is also very important. The

draft of suitable constructional material for the production of the constructional part is often in

the relation with the mechanical stressing conditioned also by the fulfilment of the

requirements for the form of the construction part and its surface modification during the

effecting of the influence of the temperature and conditions of the surrounding environment.

Testing of the mechanical characteristics of the material on standard testing bodies is not the

only process which is very important in this relation, but also directly the simulation of the

stressing of the constructional parts according to the conditions of their technical operation.

It is not always possible to set the stress-deformational and fracture characteristics of the

constructions, which are only based on the results of the standard mechanical tests of the

material or by the simulation of the initiation of the WEAR processes and their spreading in

the volume of the construction. It is necessary to minimize the risks emerging from the

difference in the stress-deformational behaviour of the test samples and the real construction

by choosing higher coefficients of safety in such cases, or during the change of the form of

the constructional parts and during the increasing of their bearing capacity, the evaluation of

the results of the prototypes of the machines, machine parts and constructions and during the

implementation of the informational systems of reliability of the device. These all can be

very useful bases for the innovation cycle of the production, planning of semi, as well as

general repairs of the devices, such as power plant blocks, large mining aggregates or some

highly strained parts of means of transport.

A very important source of information about the stress-deformational and fracture

behaviour of large-measure, often complicatedly stressed constructions during the effecting of

WEAR processes are analyses of breakdowns and serious damages of functionally similar

constructional parts.

The methods of monitoring of the fraction areas, called fractographic analyses allow to

disclose, not only the source of the initiation of the fracture process, but also the mechanism

of its creation, the influence of the micro-structure of the material and the conditions of the

surrounding environment. The use of the methods of the fractographic analysis and its

exercise during the reconstruction of the spreading of the breach is one of the conditions for

an estimation of the real fracture behaviour of the construction. Analyses of the causes of the

breakdowns caused by the spread of the fracture processes during the period of exploitation of

the construction have a special great importance for the development of new ways of the

designing of the constructions with higher level of reliability.

An objective evaluation of the time reliability of the constructional parts and their residual

durability during the effects of the WEAR processes requires deeper knowledge about the

basis of the relation between micro-structural parameters of the constructional materials,

physical mechanisms of the initiation of the processes of WEAR and their stress-

deformational and fracture characteristics. Knowledge of these relations has its meaning not

only during the increasing of the time reliability of the constructional parts, but also during

the optimized choice of the constructional material for a given purpose of use and in its result

contribute to the decreasing of the weight of the constructional parts.

Stress-deformational and fracture behaviour of constructional parts in the relation with the

results of testing of the test samples is usually evaluated from the point of view of mechanics

of continuum. This means that the influence of localised change of stress-deformational flow

is not respected during the mechanical stress, caused by inhomogeneity of the structure or

character of the surface layers. The inequalities of the surface of the constructional parts and

inhomogeneity of the structure of technical materials result in macroscopic and local stress-

deformational and fracture characteristics of material. Because the parameters of

microstructure controlling mechanisms of initiations of WEAR processes are in their size, but

also in their spatial settings often casual, local and macroscopic stress-deformational and

fracture characteristics of the material, which are influenced by these parameters, show a

certain statistical sparsity. This, together with the way of stressing, markedly influences the

time reliability of the construction and the risks of the creation of the damage of the

construction during its using grow.

During evaluation of the mechanical stressing of the construction in the relation to the

hardiness of the material against the creation of the plastic deformation or fracture instability,

are used either analytical methods of flexibility and firmness or in the case of difficult

stressing of often form complicated constructional parts, numerical method of final elements,

which has the result either static or time changeable component of the stress-deformational

field. Straining of the constructional parts is, however, exposed to effects of many other outer

accidental influences, such as the temperature, corrosion or effects of dynamic interaction of

the surface and medium, water or gases, and components of static, but also of time changeable

stress-deformational field, show sparsity.

Similarly, even mechanical characteristics of the constructional material do not stay

changeless during the technical application and in time there comes to hardening processes

and to embrittlement of the material, which is besides structural changes themselves

influenced also by the influence of surrounding environment. This causes also the reduction

of the estimated durability of the construction. Objective evaluation of the reliability of the

construction is in these cases conditioned by the quantification of the interference of the

statistical distributions of the strength characteristics and components of the stress-

deformational field dependent on time. An application of this interference approach of the

solution of the stress and hardness during the securing of the safety of machines, parts of

machines and devices during their use is an efficient tool for preventing breakdowns, or to

significantly limit their consequences.

The present requirements on the reliability of the constructional parts are determined not

only by the economical, but also by the demanding ecological conditions of the service. This

requires a maximum accuracy, with which it is necessary to estimate the critical limit state of

the construction, to provide checks of the devices in time as well as repairs. The evaluation of

the creation of the limit state of the construction does not happen without an analysis of the

microstructure parameters and their influence on the localized damage of the structure of the

material caused by the WEAR process.

The study of the relation between the microstructure, the micro-mechanism of the WEAR

process and the macroscopic mechanical characteristics of the constructional materials is a

way to formulate the requirements for the microstructure parameters, and the technological

conditions of the production and processing of the material in the relation to the reliability of

the constructional parts, which are made from it. The methods of the study of the relation

between the microstructure and the mechanical characteristics of the constructional materials

are in the result very beneficial also during the conception of new design criteria of the draft

of the material and its structure for a given purpose of use. Because in most constructional

materials the initiation of the localized limit state has an accidental character, it is possible to

quantify the risk of loss of basic function of the material from the relation of the localised and

integral limit state, the transfer of the stress-deformational field and so set exactly the safety

of the constructional part with regard to the way of its stressing and time as well. This gives

the presumptions for an effective use of the characteristics of the constructional materials

during their technical application during collateral decreasing of the weight of the

constructional parts.

Summary of terms

After reading this chapter, the reader should understand the following terms:

Construction solution of the products

Utility properties

Diagnostic methods

Construction ultimate state

Localized damage

Construction component shape and its surface treatment

Mechanical tests

Coefficient of safety

Breach propagation

Fractographic analysis

Microstructure parameters

Stress-deformation field

Questions

Not specified.

Reference sources

There is inexhaustible amount of study references dealing with the subject of Degrading

Processes of Materials, both in Czech and in foreign languages. That is why only several

titles that are essential and useful for the study are mentioned here.

ASHBY, M. F.: Materials selection in mechanical design, Pergamon Press, Oxford, 1992.

SEDLÁČEK, V.: Neželezné kovy a jejich slitiny, SNTL, Praha, 1979.

ANDERSON, T.L.: Fracture mechanics – fundamentals and applications, CRC Press, Boca

Raton, New York, 1995.

VELES, P.: Mechanické vlastnosti a skúšanie kovov, ALFA – Vydavatelstvo technickej

a ekonomickej literatúry, Bratislava, 1985.

PLUHAŘ, J., KORITTA, J.: Strojírenské materiály, SNTL, Praha, 1977.

KLESNIL, M., LUKÁŠ, P.: Únava kovových materiálů při mechanickém namáhání,

Academia, Praha, 1975.

KNOTT, J.F.: Fundamentals of fracture mechanics, Butterworths, London, 1973.

ELLYIN, F.: Fatigue damage, crack growth and life prediction, Champan & Hall, London,

1997.

ČADEK, J.: Creep kovových materiálů, Academia, Praha 1984.

RIEDEL, H: Fracture at high temperatures, Springer, Berlin 1987.

BETTEN, J.: Creep mechanics, Springer, Berlin 2005.

POMEROY, C. D.: Creep of engineering materials, Mech. Engng. Pub., London 1978.

KOWAKA, M.: Metal Corrosion Damage and Protection Technology, Allerton Press, New

York 1990.

SCULLY, J.C.: The Fundamentals of Corrosion, 3rd edn. Pergamon Oxford 1990.

SCHWEITZER, P.A.: Corrosion and Corrosion Protection Handbook, 2nd edn., Marcel

Deker, New York 1989.

WYATT, L.M., BAGLEY, D.S., MOORE, M.A., BAXTER, D.C.: An Atlas of Corrosion and

Related Failures, andMTI Publication No. 18, St. Louis, Missouri 1987. 204

Corrosion, Metals Handbook, Ninth Edition, Vol. 13, ASM International, American Technical

Publishers Ltd., Hitchin England 1987