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DURABILITY AND DAMAGE TOLERANCE 35 OF FIBROUS COMPOSITE SYSTEMS Ken Reifsnider

35.1 DEFINITIONS AND ISSUES

Durability and damage tolerance are critical to the design of composite structures. Damage tolerance is the approach often required for the certification of safety-rated structures such as aircraft components; durability has been identified as one of the most important technical drivers for the design of major composite structures such as the High Speed Civil Transport. Recent reports from the National Materials Advisory Board and a great volume of other literature focus on these

Of course, there are many nuances in the definitions of durability and damage tolerance. However, the basic concepts are quite

simple, and are illustrated in Fig. 35.1. Damage tolerance is the remaining strength after some period of service, and durability, in general, has to do with how long the component will last, i.e. with the life of the structure. In this context, durability is often discussed in terms of the resistance or susceptibility to damage initiation. Both concepts imply that the subject component is being exposed to applied conditions such as mechanical loading and environments such as temperature and chemical agents over long periods of time that are typical of the projected service life of the component.

There are several technical concepts that form a foundation for our discussion of these closely related topics. The first of these is the

1

Normalized stress level

Time / Cycles

Damage Tolerance (Remaining strength)

Life Locus Durability (Life) 4

Handbook of Composites. Edited by S.T. Peters. Published in 1998 by Chapman & Hall, London. ISBN 0 412 54.020 7

Fig. 35.1 Basic definitions of ’durability’ and ‘damage tolerance’.

Definitions and issues 795

question of the relationship of material strength to structural strength. In general, the strength of (fiber reinforced) composite materials is represented by an array of values that reflect the anisotropic nature of the materials (Fig. 35.2). For planar materials, at least the tensile strength and compressive strength in the fiber direction and transverse to the fibers and the in-plane shear strength are required for a complete answer to the question of ’how strong is this material’. However, as an array, those values do not directly show ’how strong is a composite structure’. Several possible answers to that question are typically given. One may use a ’failure criterion’ that compares all of the point stress components with all of the material strength components (such as the Tsai-Hill or Tsai-Wu riter ria)^ in some collec- tive form based on concepts such as critical energy, critical shear resistance, etc. The salient point to be made is that the complexity of (inhomogeneous) composite materials and their array of anisotropic material strengths give rise to the development of a correspond- ing array of damage and failure modes in these materials that must be understood and correctly modeled to answer the question of

’how strong is this composite structure’, even if the array of material strengths are known (shown in Fig. 35.2). Hence, there is a need to develop understandings and representations of the critical damage and failure modes that control the performance of engineering components. This technology is currently incomplete, but discussions of those topics will follow.

A second fundamental concept is microstructural architecture. As shown in Fig. 35.3(a), many fibrous composite components are made in layered or laminated form, with the fibers in different layers having different directions; in some cases the plies are made from different materials to form a ’hybrid’ composite. In addition, the fibers may not be straight, but may be woven, braided, or arranged in mats of various types (Fig. 35.3(b),(c)). These details have a major influence on the durability and damage tolerance of the materials. In fact, most composite material systems are ‘designed’ to be ’fiber dominated’, to take advantage of light, strong and stiff (but brittle) fiber materials that are available. Typically, the fibers, their geometry and their arrangement are important parts of the question.

Five in-plane strength values for fiberous composites:

Tension and compression strength in the direction transverse to the fibers Yt orY,

Tension and compression strength in the fiber direction Xt or X,

in-plane shear strength

- S

f 1 Strength tensor:

Composite * I L - k r Fig. 35.2 Schematic illustration of ’principal strength’ directions in a unidirectional continuous fiber composite laminate.

796 Durability and damage tolerance offibrous composite systems

Fig. 35.3 Typical engineering composite reinforcement types: (a) fibrous, unidirectional pile; (b) fibrous woven; (c) fibrous, braided.

A third technical issue has to do with the degradation of intrinsic strength and stiffness. For metals, the material stiffness and strength are generally constant during the life of the engineering component. This may not be true for composites. Stiffness changes of the order of 10-20% may be caused by micro-cracking, for example. Since many structures are stiffness designs, this mode of degradation must be considered. In addition, the intrinsic material strengths (indicated in Fig. 35.2) may also be degraded, especially by such things as physical or chemical aging. This behavior must also be part of the supporting predictive technology developed for these materials. Nondestructive methods of tracking such degradation are under development, but this remains as a challenge currently.

Methodologies for the assessment and prediction of durability and damage tolerance of composite materials typically involve the following features:

0 Remaining strength and life models are developed and predictions are made for each independent failure mode (such as fiber failure in tension or micro-buckling in compression, etc.).

0 Mechanics representations of the state of stress and state of material are constructed on the basis of a 'representative volume' of the material that is typical of the distributed damage state that controls the remaining stiffness and strength of the composite. A typical representative volume of material is a controlling ply in a laminate, but may be a micro-buckling ligament, a small group of fibers, etc.

0 Various methods are used to characterize and monitor the rate of strength degradation in composites. A typical parameter which is useful for that purpose is stiffness change; however, that parameter is not appropriate in some cases.

0 Micromechanics (mechanics analysis at the

Damage modes and failure modes 797

fiber/matrix level of representation) is increasingly used for remaining-strength modeling, for the calculation of stiffness change (which leads to internal stress redistribution), and for the estimation of remaining strength for a given failure mode. Statistical considerations are essential for the correct representation of the long-term behavior of composites. Composites typically fail because of the statistical accumulation of defects, which eventually interact to create a critical condition. This is in contrast to self-similar single crack prop- agation that is the typical mechanism of failure for common metals. Time-dependent behavior such as viscoelastic creep, creep rupture (driven by such things as internal stress redistribution or oxidation), and aging are typically important in the consideration of the long- term durability and damage tolerance of polymer composites, particularly for components that serve at elevated temperatures.

This chapter will discuss the range of physical and engineering details that define and control this subject. Of course, a complete discussion would fill several volumes, so the reader should regard this discussion as only a starting point for further study.

35.2 DAMAGE MODES AND FAILURE MODES

The failure of 'typical' (homogeneous isotropic) engineering materials is a familiar topic. The subjects of ductile rupture and brittle fracture are widely discussed and taught in undergraduate and graduate courses. However, composite materials generally do not behave in a manner easily described by either plasticity (or yield) theory or by self- similar crack growth concepts.

The reason for this different behavior is the fundamental difference in the micro-structure of composite materials, i.e. in the way they are

made. Composites consist of mechanical 'mix- tures' of distinct phases (such as fibers or particles) in a matrix material. The geometry and arrangement of the reinforcement phase is carefully chosen to achieve the desired composite properties. As a result, such material systems are always inhomogeneous, often anisotropic, and often brittle. These three basic characteristics control the nature of damage development and failure in composite materials.

The most salient single feature of damage in composites is the process of damage accumulation. Damage development usually involves many damage modes which create a widely distributed damage state, and failure is usually the result of a statistical accumulation of damage (rather than the statistical occurrence of damage). As discussed below, these multiple damage accumulations on failure modes are often closely related to the manner in which the composite is made, especially to the basic nature of the inhomogeneity and anisotropy of the material. This damage development process ultimately controls durability and damage tolerance, so we will discuss some typical major features of that phenomenon.

The most pervasive damage mode in composite materials is microcracking, most often in the matrix material. Figure 35.4 shows two embodiments of this mode. Figure 35.4(a) shows an X-ray radiograph of a cross-ply laminate with cracks in both ply types, and Fig. 35.4(b) shows matrix cracking parallel to the fibers in the off-axis plies of a laminate, as seen from a tracing of those cracks as they appear on the edge of this [0,45,45,90Is laminate. A typical scenario for the development of such cracks is the formation of matrix cracks as a function of increasing applied load or increasing cycles of loading. These cracks typically extend through the thickness of a ply and generally extend quickly in the fiber direction if the local stress is uniform.

Several other important features of matrix cracking are suggested by Fig. 35.4. As shown by Fig. 35.5, matrix crack formation releases


"'r!

. I :

'r!

I rt

.1!

I

-.e-

b

Fig. 35.4 Microcracking in the matrix, parallel to the fibers; a radiograph of a cross-ply laminate with (a) inter-ply delamination at crack intersections (arrow) and (b) a tracing of matrix cracks on the edge of a [0,+45,-45,90] laminate.

stored energy in the cracked ply or material, and changes the stiffness of material propor- tionately, a matter of concern to engineering applications, as noted earlier. However, the density of cracks in the ply of a laminate reaches a stable saturation value, as first observed by Reifsnider et a1.5,8, called the characteristic damage state (or CDS) of the ply. That CDS is a function only of the properties of the plies, their thickness, and their stacking sequence. Figure 35.6 shows that the same CDS is formed by static or cyclic loading. This CDS can be readily predicted since the crack spacing is determined by the rate at which the surrounding material can transfer stress back into the broken ply. Moreover, the stiffness change caused by this cracking can also be predicted as well7r9-*l.

A second important damage mode is delamination, as shown in Fig. 35.7. Delamination is driven by the fact that local regions of the composite would deform differently in response to

Strain

Fig. 35.5 Change in slope of the elastic stress-strain curve induced by microcracking.

APPLIED STRESS (MPo) 100 200 300 400 500 600 m

I I I I

01 I I I I 0 0.2 0.4 0.6 0.8 I .o

NO. OF CYCLES (MILLIONS)

Fig. 35.6 Data showing identity of the equilibrium crack spacing ('characteristic damage state' or CDS) for quasi-static and cyclic loading of a laminate.

the local loads if they were not bonded together in the composite. Hence, stored energy is released if they separate, and that energy drives the separation process. The most common example of this damage mode is the separation of the plies of a laminate near a free edge, as shown in Fig. 35.7. This process has been widely studied and is well described. More will be said of this driving mechanism below.

It should be noted that delamination is usually nucleated by other damage modes (such as matrix and although it is a common damage mode, it is not usually a failure mode, per se. Delamination usually begins

Damage modes and failure modes 799

fW"82tr'tiKT W 7 K " V q T 4 ~ K ~ W m ~ T matrix cracks in one ply may cause fiber fracture in an adjacent ply due to the local stress concentrations21,2z.

Figure 35.8@) shows a second feature of importance. When the matrix and fibers have comparable stiffness and strength, the fibers may break many times along their length before the composite fractures. In this situation, fiber fracture can cause a significant stiffness loss as well as a strength reductionu.

Another generic damage mode is micro- 1 buckling, induced by local or global compressive loads, as shown in Fig. 35.9.

I -7 '

Fig. 35.7 Edge micrograph of delamination (arrow) showing (a) relationship to matrix cracking; (b) plan view radiograph of edge delamination in a cross- ply laminate (shaded regions).

at an edge, such as a cutout, bolt hole, rivet hole, etc. If it is in a region of nonuniform stress, it may stop growing when it reaches the boundary of that region. Even if it grows to large dimensions, it usually does not cause significant loss of strength in engineering sized structures. Still, the loss of integrity can lead to other damage and failure modes, so it should be avoided.

A third generic damage mode is fiber fracture. Many composites are 'fiber dominated', i.e. they depend on the fibers for their stiffness and strength. Hence, fracture of the fibers is both an important damage mode and failure mode. However, fiber fracture is difficult to detect and has been studied less completely than many other damage modes. However, considerable data have been ~ollected'~'~. Figure 35.8 shows two examples of such data, driven by two important mechanisms. Figure 35.8(a) shows fibers broken beside one another, a typical situation. In many composites, the fibers are coated with a material that decreases the tendency for the fracture of one fiber to cause the fracture of neighboring fibers by forming an 'interphase region' around the fibers that tends to 'isolate' the fracture effectslS2O. It is also important to note that the


There are several aspects of this phenomenon that are of importance to durability and damage tolerance. For example, the compression strength (or remaining strength) of the composite may be controlled by the local stress required to initiate the local instability, in which case one wants a large diameter, stiff fibers in a stiff matrix. Or, the strength may be controlled by local resistance to shear deformation after buckling begins, in which case one would choose a tough matrix or interphase region between the fibers and the matrix. This is another case in which a damage mode may or may not be a failure mode, an important distinction.

Fig. 35.9 Localized microbuckling in a polymer matrix composite. Printed with permission, I.M. Daniel and 0. Ishai, Engineering Mechanics of Composite Materials, Oxford University Press, Oxford, 1994.

Another 'damage mode' of considerable importance to polymer composites and all composites used at high temperatures is the phenomenon of creep, i.e. time-dependent deformation at constant applied stress. Figure 35.10 shows a typical form of that behavior, with an initial transient region, a steady state region (in which most engineering design is done), and a tertiary (usually unstable) region. This phenomenon is usually represented by introducing viscoelastic

Time

Fig. 35.10 Schematic of typical creep deformation at constant load and temperature.

or rheological models that represent the behavior in terms of a change in the stiffness of the material with time, as a function of temperature. Quite often, the reinforcing fibers do not show creep behavior at low temperatures, but at high temperatures, essentially all constituents may creep. The changes of stiffness with time can be characterized in the labora- tory, and must be modeled carefully, based on those data. In fact, this part of the behavior is critically important to the correct calculation of internal stress states, since the creep of the constituents changes the internal stress distribution greatly in some cases. For example, if the matrix creeps more than the reinforcing fibers (a typical situation), that creep 'relaxes' the stress in the matrix, and increases the load carried by the fibers. If we wish to calculate a fiber-controlled strength, for example, a correct representation of this behavior must be included in our model.

Finally, another failure mode is creep-rupture. This is a fairly general terminology used to refer to a variety of physical phenomena that produce time-dependent failure. This can be due to, say, oxidation of the fibers, or to other physical degradation processes which eventually cause rupture. It is clear that these phenomena must also be modeled correctly if we are to discuss durability and damage tolerance of material systems.

Damage drivers and damage 'resistance' 801

35.3 DAMAGE DRIVERS AND DAMAGE 'RESISTANCE'

In the previous section, a number of damage and failure modes that occur in composite materials, and ultimately control durability and damage tolerance, were identified. Many of these modes are related to the manner in which the composites were put together. This raises the basic question of 'can one design composite materials to be durable and damage tolerant?' Most of the rest of this discussion will address this question.

Some general concepts will be followed by some micro-mechanics methods of quantifymg answers. Microcracking is likely to be the most pervasive damage mode in typical composites, especially under long-term loading, and most especially under cyclic loading. Even though most matrix materials are chosen because they offer some level of ductility, in most composite systems the matrix is highly constrained so that cracks develop due to local constraint, local stress concentrations, and local defects that grow rapidly under what is generally a 'plane strain' condition. Hence, matrix toughness, in the general sense, is the key to the reduction of matrix cracking. Increasing the strain to failure of the matrix material is a pri- mary objective, and increasing the plane-strain fracture toughness of the matrix is a compan- ion objective. There is a richly developed science and technology associated with matrix toughening; some starting points are listed in Wilkinson et al.24 and Hedrick et al?5.

A second damage mode identified earlier is delamination. This problem is a strong combi- nation of structural and material concerns. The material concerns are essentially the same as those discussed for matrix cracking, with one important exception. Matrix toughness does not translate directly into interlaminar toughness. Hence, resistance to delamination cannot be controlled entirely with material property increases. The structural part of the problem does, however, present opportunities. It was mentioned before that delamination is driven

by local discontinuities in stress state, typically caused by neighboring plies or ply groups (bonded together) that would have very different strain states if they were not bonded. Hence, the orientation of the plies in a laminate and the stacking sequence of those plies are controlling players in the development of the interlaminar stresses that drive delamination. This problem has been exhaustively studied, and methods of reducing interlaminar stresses have been widely disc~ssed '~-~~, but because of the inhomogeneous and often anisotropic nature of composites, interlaminar stresses generally cannot be eliminated in laminated systems, so mechkical methods are widely used to control that tendency. The most successful of these is weaving, i.e. to use woven fiber architectures to reduce the anisotropy of a given ply, and therefore, to reduce the 'disagreement' between the response of any two or more plies. Woven materials are now widely used, especially for this reason. A second approach is to 'stitch' the composite in the region of non-uniform stress, typically near an edge of the laminate. Stitching simply 'clamps' the edge of the material to prevent it from separating; the internal stresses are still present. Stitching has a some- what smaller number of proponents, but is a successful method as well. Finally, three- dimensional reinforcement, such as mats or braids, also serve the purpose of providing constraint to the delamination drivers. These methods are not as widely used at this time, largely because of the difficulty associated with manufacturing.

A less obvious influence on durability and damage tolerance is the bonding between the fiber and matrix. The nature of this influence has only come to light in recent years. Some of the mechanics models needed for this discussion will be developed in the next section; only a few general points will be made here. First, the properties of composite materials are determined not only by the properties of the constituents, but they are also greatly influ- enced by the manner in which the constituents

802 Durability and damage tolerance of fibrous composite systems

interact. This critical interaction is, of course, controlled by the bonding between the constituents, between the fibers and matrix in our case. Typically, this bonding is ‘controlled’ by a fiber coating or ’sizing’. However, it is now known that such things as notched fatigue behavior can be improved by as much as two orders of magnitude by carefully ’designed’ ’interphase’ regions between the fibers and the matrixz6. There are at least two basic concepts operating in these effects. First, if one can toughen the composite by toughening the interphase between the fibers and matrix, the composite is likely to be more durable, as discussed above. Second, the interphase region can greatly influence the local stress state, and reduce the driving force for fiber-matrix debonding. An illustration of that is shown in Fig. 35.11. If one considers the strength of a composite under loads applied perpendicular to the fiber direction, then it is clear that the fiber causes a local stress concentration, in pro- portion to the difference between its properties and those of the matrix. However, if a coating around the fiber is introduced, this local concentration can be greatly reduced. In fact, for a ’rigid’ fiber, compared to the matrix, it is not surprising that a compliant coating on the fiber will increase the transverse composite strength by as much as a factor of two, and the

Interphase region

Composite

Fig. 35.11 Schematic diagram of the geometry of the interphase region in a fibrous composite, sub- iected to loading. transverse to the fibers.

strain to failure by as much as a factor of In general, although design rules are

not yet fixed, design of the interphase region is a new and important opportunity for the enhancement of the durability and damage tolerance of composite system^^^^*.

The final subject in this section is ’failure criteria’; which are used to describe remaining strength. In general, failure criteria are chosen on the basis of the known failure mode. If fiber fracture controls strength, then a suitable criterion may be just the stress in the fiber direction divided by the strength in that direction. If matrix behavior is controlling, a shear stress or combined stress criterion may be appropriate. Figure 35.12 shows a comparison between strength ‘envelopes’ predicted by two popular criteria. It is important to note that the inputs to the failure function will, in general, change as a function of time and loading history. The general form of any failure criterion will usually be some function of the ratios of stress in principal material directions to strength in those directions, as mentioned earlier. Under long-term conditions which induce damage, the local stress changes as damage causes redistribution, and the principal values of material strength change, due to such things as constituent degradation or micro-damage. Hence, to calculate damage tolerance by using

Criterion: I----- Maximum stress

Applied Stress (ksi)

0 90 Angle of Loading (deg)

Fig. 35.12 Allowable uniaxial loading as a function of angle of loading relative to the fiber direction in a unidirectional lamina, estimated from a maxi-

” mum stress and a popular effective stress criterion.

Composite micro-strength and remaining strength models 803

failure functions (or criteria) to calculate remaining strength, one must be careful to use the correct local stress state and material state in those expressions, especially when degradation has changed those states from their initial values.

35.4 COMPOSITE MICRO-STRENGTH AND REMAINING STRENGTH MODELS

The importance of material principal strengths was noted, and the importance of composite microstructure in the determination of those strengths has been emphasized. The properties, geometry, arrangement, and bonding of the constituents determine the resulting values of composite principal strengths. So, if those factors are understood, strong, durable, damage tolerant composites can be designed. That understanding is currently incomplete, but some models are available. Such models are very valuable since they can tell us the preferable way to make composite materials, in contrast to how they can be made (the job of the materials science community).

In this limited space, one example will suf- fice to demonstrate the general nature and

utility of such models. The example is a recent model of tensile strength. (Figure 35.13). The stress in the broken fibers builds back up to the undisturbed level by shear transfer from the surrounding matrix, composite, and interphase region. That rate of buildup is directly proportional to the stress concentration in the next nearest fibers; if the buildup occurs over a short distance (a short 'ineffective length), the stress concentration in the neighboring fibers is great, and they tend to break causing very brittle composite behavior. However, if the buildup occurs over a large distance (i.e. if the material around the fiber is very compliant or breaks easily ), the strength of each fiber is lost completely when the first local fiber break occurs. A model has been developed that describes the physics and mechanics of this behavior, which estimates the fiber strength as:

2z0L l /m+l 2 l / m + l m + 1 4 = ...'-+1(7r) ( K T ) m + 2

(1 + m)l/" (C," + q m - 1 + ... + ly" (35.1)

where a, is the Weibull characteristic strength of the fibers, z, is the shear stress between the

Composite

FlbersC

Fiber breaks E

4 zt: Normal stress In:

E t broken fiber

: P nelg h boring

. I Average global values away from fiber fracture

Fig. 35.13 Schematic diagram of the local stress distribution around broken fibers in a unidirectional composite.


fibers and the matrix (usually taken as the interphase strength), m is the Weibull shape parameter for the fiber strength distribution, and Cn is the local stress concentration when n fibers are broken together in a local region. Hence, the tensile strength in the fiber direction can be estimated on the basis of the properties of the constituents and the interphase region between the fibers and the matrix. If any of those constituent characteristics change, the model can show how the strength of the composite changes, i.e. the model can be used to calculate the damage tolerance of the composite if the failure mode is controlled by fiber strength in tension. Comparable models can be constructed for compression failure, and for other failure mode^^*^^.

35.5 ESTIMATION OF REMAINING STRENGTH AND LIFE

As indicated earlier, damage tolerance is defined by remaining strength, and durability is usually discussed in terms of life. In this final section, one approach to the estimation of the durability and damage tolerance of

continuous fiber reinforced composites is outlined. A great many details will have to be omitted due to space limitations; the inter- ested reader can find them in other publication^"^^.

A start is to identdy a well-defined failure mode, as defined earlier. Since damage is distributed, this damage mode will be 'typical' of any 'representative volume' of material; a mechanics boundary value problem on such a representative volume (RV), as suggested in Fig. 35.14 can be 'set'. This RV may be discon- tinuous; i.e. it may have cracks, delamination, debonds, etc. But some part of it will remain intact until fracture of the composite, and this part of the RV that defines the fracture event is a 'critical element'. Therefore the objective is the calculation of the state of stress and state of material in the 'critical element.' One can write all failure functions, Fa, in that critical element, and claim that when these failure functions (for each distinct failure mode) predict failure, the composite will fail.

Invoking kinetic theory we can derive an equation that relates changes in stress state and material state with time and loading history to remaining strength, i.e. allow the incorporation

failure modes

Fig. 35.14 Diagram illustrating how experimental observation of failure modes define the representative volume (used to set the boundary value problem) and the critical elements in which all continuum states are defined.

Estimation of remaining strength and life 805

of the explicit time, cycles, and environmental dependence that leads to phenomenological behavior such as creep, creep rupture, fatigue, and aging into the calculation of remaining strength. From thermodynamic principles, the following expression can be derived:

F, = 1- lyl(l - Fa),( N) n 1-1 d( $) (35.2)

where

in the critical element, F, is the normalized remaining strength, n is cycles, and N is the life of the critical element under the current state of stress and state of material. The methodology of this calculation is shown in Fig. 35.15. Remaining composite strength, F , is calculated directly; life is calculated by the coincidence of Fa and Fr. Numerous comparisons of such calculations with experimental data have been made over the last 10 years or so, and there are a few examples at the end of this chapter. The immediate purposes are served by using eqn(35.2) to examine the effects of some hypothetical change in material state and stress state on remaining strength (damage tolerance). If the failure mode is ten-

sile fiber failure, and it is assumed that some fatigue behavior of unidirectional material under uniaxial stress in the fiber direction has been measured, a 1-D SN relationship can be derived, of the form:

s, = A + B (log N ) p (35.3) S"

where, for our example, A = 1, B = -0.1, Su = 100 ksi (the initial ultimate strength), p = 1, and Sa is the applied stress amplitude. Equation (35.3) provides an input, N, into (35.2) since

where u,, is now the current local ply stress in the fiber direction, and X , is the current local principal material strength in tension, given by eqn (35.1). Substituting eqn (35.4) in eqn (35.2) and assuming that no other phenomena are present (and using j = 1.2, a known typical value), the curve (a) in Fig. 35.16 results. Now, suppose the ply is the critical element in a multiaxial laminate having off-axis plies that crack and 'dump' stress into the critical element as a function of

State of State of I I

life N, N2

Subcritical Critical reipresentative volume

Fig. 35.15 Schematic flow diagram of the manner in which the MRLife simulation scheme calculates remaining strength and life.


Remaining I Strength

-

I

Cycles Cycles

Fig. 35.16 Calculated remaining strength predictions for (a) 0" lamina degradation alone; (b) added effect of matrix cracking; (c) added effect of fiber degradation (e.g. by oxidation).

Fig. 35.18 Assumed degradation of fiber strength for the sample laminate.

cycles, according to the rate shown in Fig. 35.17 (from cracking rates that must be measured or estimated). With this internal stress redistribution, only, added to eqn (35.2), the damage tolerance changes to curve (b) in Fig. 35.16. Of course, if creep occurs in the matrix (perhaps because of increased temperature), in which case the local fiber stress will increase again as a function of cycles to change the form shown in Fig. 35.17. Finally, suppose creep rupture is occurring, driven, for example, by oxidation of the fibers that is reducing the diameter of the fibers, D, in eqn (35.1), in the manner shown in

Stress increase due

Direction Fiber-

Stress

I I 40 ' 4 4

1 5x10 9.999~10 Cycles

Fig. 35.17 Assumed increase in stress in the 0" ply due to matrix cracking.

Fig. 35.18. Then the strength model, eqn (35.1), correctly integrates that micro-change into the global calculation, and eqn (35.2) shows the damage tolerance to be curve (c) in Fig. 35.16 for that situation. Hence this 'micro-kinetic' approach has the capability to estimate durability and damage tolerance for very complex situations involving combinations of many time and cycle dependent phenomena in composite systems, using a mechanistic approach.

An example follows. Using the methods described above, the rate of matrix cracking and the unidirectional SN curve of a carbon fiber reinforced PEEK matrix composite were determined, and used to estimate the remaining strength and life of several different laminates made from that material. Figure 35.19 shows an example of the predicted and observed life for several load levels of a quasi- isotropic laminate made from such material and Fig. 35.20 shows comparisons of the predicted and observed remaining strength of such laminates for two load levels and cycles of load application. It can be seen that this approach can produce quite useable results. Many such predictions have been compared using the MRLife performance simulation code based on this

Estimation of remaining strength and life 807

......................................................

.....................................................

AS-4lPEE K (APC-2) Quasi-Isotropic Notched Fatigue (R=-1)

0.75

0.45 I 1 I 3 4 5 6 7

Log N (Cycles) Simonds B Stinchcomb MRLife

(1 989) Prediction 0

Fig. 35.19 Predicted (line) and observed life for a quasi-isotropic AS-4/PEEK notched coupon under fully reversed loading.

11.05

1 .00 r F 3 0.95

P 2

E! 5

.- ; 0.w

0 z

0.85

0.80

Residual Strength at 0.70 Suit Residual Strength at 0.90 S ,,I 1.05

1 .w r P 3 0.05

P d x 1 0.w

€

E! 5

N

0 z

0.85

0.80

Cycles M E h E x p e p n t

......................................................

2 5 1 0 2 0 5 0 1 0 0 2 0 0

Cycles Mfih Expepml

Fig. 35.20 Predicted (lines) and observed residual strength of AS-4/PEEK specimens subjected to under fully reversed cyclic loading.


35.6 SUMMARY

This has been a short outline of the physical behavior associated with the durability and damage tolerance of composite material systems, and a few modeling approaches to the estimation and prediction of that behavior have been indicated. It should be noted that there is every evidence that composite materials are remarkably durable and damage tolerant. Fatigue allowables for carbon fiber reinforced polymer composites, for example, exceed those of structural steels, and the durability and damage tolerance of ceramic composites make them the only choice for ultra-high temperature applications in turbines, etc. Understanding of this subject, which is admittedly incomplete, has reached a level that is sufficient to support engineering applications of composites to even the most demanding situations in the most severe environments. In fact, that is exactly the situation in which the application of composites is most beneficial and cost effective. Composite material systems can provide many new opportunities to design for damage tolerance and durability.

REFERENCES

1.

2.

3.

4.

5.

Life Prediction Methodologies for Composite Materials, NMAB-460. Washington, D.C.: National Academy Press, 1990. High-Temperature Materials for Advanced Technological Applications, NMAB-450. Washington, D.C.: National Academy Press, 1988. Horton, P.E. and Whitehead, R., Damage Tolerance of Composites, Vol. I and 11, Air Force Wright Aeronautical Laboratories, AFWAL TR-

Daniel, I.M. and Ishai, O., Engineering Mechanics of Composite Materials. New York: Oxford Univ. Press, 1994. Reifsnider, K.L. and Highsmith, A.L., Characteristic damage states: A new approach to representing fatigue damage in composite laminates. In Materials: Experimentation and Design in Fatigue, Guildford, U.K.: Butterworth/IPC, 1981, pp. 246-260.

87-3030, 1988.

6. Damage in Composite Materials: Basic Mechanisms, Accumulation, Tolerance, and Characterization, STP 775, American Society for Testing and Materials, (ed. K.L. Reifsnider), 1982.

7. Highsmith, A.L., Stijfrzess Reduction Resulting from Transverse Cracking in Fiber-Reinforced Composite Laminates. Master of Science Thesis. Blacksburg, Virginia: Virginia Polytechnic Institute and State University, 1981.

8. Reifsnider, K.L., Some fundamental aspects of the fatigue and fracture of composite materials. In Proc. 14th Ann. SOC. Engng Science Mg. Bethlehem, PA: Lehigh University, 1977.

9. Highsmith, A.L., Damage Induced Stress Redistribution in Composite Laminates. PhD Dissertation. Blacksburg, Virginia: Virginia Polytechnic Institute and State University, 1984.

10. Bader, M.G., Bailey, J.E., Curtis, P.T. and Parviz, A., The Mechanisms of Initiation and development of damage in multi-axial fibre-reinforced plastic laminates. In Proc. 3rd Intern. Conf. Mechanical Behavior of Materials. Cambridge, U.K., 1979.

11. Reifsnider, K.L., Damage and damage mechanics. In Fatigue of Composite Materials, (ed. K.L. Reifsnider), Amsterdam: Elsevier Science Publishers, 1990.

12. OBrien, T.K., Characterization of delamination onset and growth in a composite laminate. In Damage in Composite Materials, ASTM STP 775, 1982, p. 140.

13. OBrien, T.K., Analysis of local delaminations and their influence on composite laminate behavior. In Delamination and Debonding of Materials, ASTM STP 876, 1985, pp. 282-297.

14. OBrien, T.K. and Hooper, S.J., Local delamination in laminates with angle ply matrix cracks: Part I, Tension tests and stress analysis. In N A S A TM 104055,1991.

15. Razvan, A. and Reifsnider, K.L., Fiber fracture and strength degradation in unidirectional graphite/epoxy composite materials. In Theoretical and Applied Fracture Mechanics, 1991,

16. Razvan, A., Bakis, C.E. and Reifsnider, K.L., SEM Investigation of fiber fracture in composite laminates. In Materials Characterization, 1990,24,

17. Lorenzo, L. and Hahn, H.T., Fatigue failure mechanisms in unidirectional composites. In Composite Materials: Fatigue and Fracture, ASTM STP 907, American Society for Testing and Materials, Philadelphia, PA, 1986, pp. 210-232.

16,81-89.

179-190.

References 809

18. Ishida, H. (ed.), Controlled Interphases in Composite Materials, New York: Elsevier, 1990.

19. Warren, R. (ed.), Ceramic Matrix Composites, New York: Chapman and Hall, 1992.

20. Reifsnider, K.L. (ed.), Fatigue of Composite Materials, London: Elsevier Science Publishers, 1991.

21. Jamison, R.D., Fiber fracture in composite laminates. In Proc. lntl. Con$ on Composite Materials VI, 1987, no. 3, pp. 185-199.

22. Jamison, R.D., Schulte, K., Reifsnider, K.L. and Stinchcomb, W.W., Characterization and analysis of damage mechanisms in tension-tension fatigue of Graphite/Epoxy Laminates. In Efects of Defects in Composite Materials, ASTM STP 836, American Society For Testing and Materials, Philadelphia, PA, 1984, pp. 21-55.

23. Tiwari, A., The Development of an Interpretive Methodology for the Application of Real-Time Acousto-Ultrasonic NDE Techniques for Moni toring Damage in Ceramic Composites Under Dynamic Loads. PhD Dissertation. Blacksburg, Virginia: Virginia Polytechnic Institute and State University, 1993.

24. Wilkinson, S.P., Liptak, S.C., Lesko, J.J., Dillard, D.A., Morton, J., McGrath, J.E. and Ward, T.C., Toughened bismaleimides and their carbon fiber composites for fiber-matrix interphase Studies. In Proc. 6th Japan-U.S. Conf Composite Materials, 1992.

25. Hedrick, J., Patel, N.M. and McGrath, J.E., Toughening of epoxy resin networks with func- tionalized engineering thermoplastics. In ACS Advances in Chemistry Series, no. 233, Toughened Plastics I: Science and Engineering, (eds. C.K. Riew and A.J. Kinloch), 1993, pp. 293-304.

26. Swain, R.E., Reifsnider, K.L., Jayaraman, K. and El-Zein, M., Interface/interphase concepts in composite material systems. J. Thermoplastic Comp. Mater., 1990, 3, 13-23.

27. Case, S.W., Micromechanics of Strength-Related Phenomena in Composite Materials. MS Thesis. Blacksburg, Virginia: Virginia Polytechnic Institute and State University, 1993.

28. Carman, G.P., Eskandari, S. and Case, S.W., Analytical investigation of fiber coating effects on shear and compression strength, symposium on durability and damage tolerance, ASME WAM, (in press), 1994.

29. Jayaraman, K. and Reifsnider, K.L., The interphase in unidirectional fiber-reinforced epoxies: effect of residual thermal stresses. Comp. Sci. Tech., 1993,47, 119-129.

30. Jayaraman, K., Gao, Z . and Reifsnider, K.L., The interphase in unidirectional fiber reinforced epoxies: effect on local stress fields. J. Comp. Tech. Res., 1994,16(1): 21-31.

31. Jayaraman, K., Reifsnider, K.L. and Swain, R.E., Elastic and thermal effects in the interphase: Part 11. comments on modeling studies. J. Comp. Tech. Res., 1993,15(1):14-22.

32. Jayaraman, K., Reifsnider, K.L. and Swain, R.E., Elastic and thermal effects in the interphase: Part I. comments on characterization methods. J. Comp. Tech. Res., 1993,15(1): 3-13.

33. Gao, Z . and Reifsnider, K.L., Micromechanics of Tensile Strength in Composite Systems. Fourth Volume, ASTM STP 2256, (eds W. W. Stinchcomb and N. E. Ashbaugh), Philadelphia, PA: American Society for Testing and Materials, 1993, pp. 453-470.

34. Xu, Y. and Reifsnider, K.L., Micromechanical modeling of composite compressive strength. J. Comp. Mater., 1993, 27(6): 572-587.

35. Reifsnider, K. L. and Gao, Z., Micromechanical concepts for the estimation of property evolution and remaining life. In Proc. Intern. Con5 Spacecraft Structures and Mechanical Testing, Noordwijk, the Netherlands, 1991, pp. 653-657.

36. Curtin, W.A., Theory of mechanical properties of ceramic-matrix composites. J. Amer. Ceram.

37. Reifsnider, K.L., Performance simulation of polymer-based composite systems. In Durability of Polymer-Based Composite Systems for Structural Applications, (eds A.H. Cardon and G. Verchery), New York: Elsevier Applied Science, 1991, pp. 3-26.

38. Reifsnider, K.L. and Stinchcomb, W.W., A critical element model of the residual strength and life of fatigue-loaded composites coupons. In Composite Materials: Fatigue and Fracture, ASTM STP 907, (ed. H.T. Hahn), Philadelphia, PA: American Society for Testing and Materials,

39. Reifsnider, K.L., Use of mechanistic life prediction methods for the design of damage tolerant composite material systems. In ASTM STP 2257, (eds M.R. Mitchell and 0. Buck), Philadelphia, PA: American Society for Testing and Materials,

40. Reifsnider, K.L., Evolution concepts for microstructure property interactions in composite systems. In Proc. IUTAM Conf. Microstructure-Property Interactions in Composite Materials. Aalborg, Denmark, 1994.

SOC., 1991, 74(11), 2837-2845.

1986, pp. 298-313.

1992, pp. 205-223.

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