grain size effects in micro-forming: an experimental analysis · the goal of this project is rstly...

Grain size effects in micro-forming:an experimental analysis

Peter JanssenMaster Thesis, MT 03.04

supervisor: Prof. Dr. Ir. M.G.D. Geerscoach: Dr. Ir. W.P. Vellingacommission: Dr. Ir. Th. H. de Keijsercommission: Dr. Ir. B. Kooi

Eindhoven University of TechnologyFaculty of Mechanical EngineeringMaterials Technology Group

Eindhoven, March 2003

Contents

Summary iii

Samenvatting iv

1 Introduction 1

2 Theoretical considerations 22.1 Plastic deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 Size-effects in tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3 Size-effects in punching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3 Micro-forming of Al foils 93.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.2 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.2.1 Rolling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2.2 Recrystallisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.3 Mechanical behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.3.1 Tensile experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.3.2 Punching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.3.3 Drawing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4 Multi Axial Compression 244.1 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.1.1 LN1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.1.2 Al 51st heat-treated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.2 Mechanical behaviour of MAC samples . . . . . . . . . . . . . . . . . . . . . . . . 304.2.1 LN1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.2.2 Al 51st . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5 Conclusions 34

6 Recommendations 36

A Sample preparation 38

B Experimental data 40

C Microstructures of MAC samples 41

Summary

The goal of this project firstly is to investigate grain size effects in micro-forming, and secondlyto investigate grain size effects for ultra fine grained material that has been produced by severeplastic deformation.

To investigate size-effects in micro-forming tensile, punching and drawing experiments havebeen conducted on pure Al sheets and commercial Al foil. These Al sheets and foils have beenheat-treated to obtain varying ratios between sample thickness and grain size (

��). The recov-

ery and recrystallisation treatments, at temperatures of 100 �� to 600 �� , resulted in a meangrain size from 1 �� up to 870 �� , and

��between 0.3 and 60.

Tensile experiments for both samples showed a decrease in flow stress with increasing grainsize. The material seems to behave according to the Hall-Petch relation, an specific surfaceeffect of the increased surface could not be observed. A deviation from the general macro-scopic behaviour has been found for the ductility. At increasing grain size the ductility firstlyincreases then decreases for

��about 3. Most likely the importance of the mechanical properties

of the weakest grain on the material behaviour increases. The deformation concentrates on thisweakest grain and the ductility will decrease.A decrease of the maximum shear strength in punching and of the maximum punching forcein drawing has been observed. This can again be attributed to the decreasing specific grainboundary area with increasing grain size. The deviation between the measurements increasesat increased grain size. This can be understood considering that the ’average’ orientation of thegrains in the deformation regions varies stronger for the specimens with increasing grain size.The punch displacement at maximum shear strength shows an increase followed by a decrease.This is in agreement with the results in tension for the ductility.

The multi axial compression (MAC) technique has been used to produce severely plasticallydeformed material with ultra fine grains, using recovery and recrystallisation treatments thegrain size has been changed. Compression results of the as-deformed and recrystallised speci-mens, with a submicron grain size, show a high flow stress in combination with a high ductility.For these samples the strain hardening effect is lost. To draw final conclusions on the materialbehaviour tensile data is necessary.The recrystallised samples showed typical behaviour for coarse grained material, a relative lowflow stress with significant strain hardening.

Two deviations from the general macroscopic behaviour have been found. Firstly a decreasein ductility has been observed with increasing grain size and decreasing

��for experiments on

thin Al sheets. Secondly, there is an indication of is a combination of a high flow stress and ahigh ductility for severely plastically deformed material having a submicron grain size.

Samenvatting

Het doel van dit project is ten eerste het onderzoeken van de invloed van de korrelgrootte bijmicro-omvormen en ten tweede wordt de invloed van de korrelgrootte onderzocht voor sam-ples die gemaakt zijn met behulp van multi axiale compressie.

Om schaal effecten bij micro-omvormen te onderzoeken worden trek, pons en dieptrek exper-imenten uitgevoerd op Al folies. Deze folies zijn warmte-behandeld om een vari �

� rende ratiotussen sample dikte en korrelgrootte (

� �) te verkrijgen. Deze herstel- en rekristallisatie behan-

delingen, tussen de 100 �� en 600 � � , resulteerden in korrelgroottes van 1 �� tot 870 �� .In trek is er een afnemende vloeispanning gemeten als de korrelgrootte toeneemt, wat in overeen-stemming is met het algemeen bekende macroscopisch gedrag. Het materiaal blijkt zich tegedragen volgens Hall-Petch. Een afwijking van het macroscopisch gedrag is gevonden voorde ductiliteit. Na een toename neemt deze af als

� �kleiner dan 3 wordt. Het meest aannemelijk

is dat de mechanische eigenschappen van de zwakste korrel een grotere invloed krijgen op hettotale gedrag. De deformatie zal zich op deze zwakste korrel concentreren, waardoor het ma-teriaal eerder zal falen.Een afname in maximale afschuifsterkte bij het ponsen en stempelkracht bij het dieptrekken zijngemeten bij toenemende korrelgrootte. Net als voor de afname van de vloeispanning kan dittoegeschreven worden aan de afname aan korrelgrens-oppervlak, er zijn minder obstakels diede beweging van dislocaties hinderen. De verschillen tussen de metingen van dezelfde sample-set nemen toe met toenemende korrelgrootte. De ’gemiddelde’ ori �

� ntatie van de korrels in dedeformatie zone zal sterker vari �

� ren als de korrelgrootte groter is. Voor de stempelverplaatsingbij maximale afschuifsterkte is een toename gevolgd door een afname gemeten bij toenemendekorrelgrootte. Dit materiaal gedrag is in overeenstemming met de resultaten gevonden voorde trekproeven.

De multi axiale compressie methode is gebruikt om een ander soort samples te maken, met be-hulp van warmtebehandelingen zijn de korrelgroottes gevarieerd. Het mechanisch gedrag isgemeten met compressie en hardheidsmetingen. Voor de gedeformeerde en herstelde samples,met een submicron korrelgrootte, is een combinatie van een hoge vloeispanning en ductiliteitgemeten. Gewoonlijk is een hoge vloeispanning gekoppeld aan een lage ductiliteit. Deze sam-ples vertoonden ook geen rekversteviging. Om sluitende conclusies omtrent de ductiliteit tetrekken is het nodig om aanvullende trekproeven te doen.Voor de gerekristalliseerde samples wordt het typische gedrag voor grof korrelig materiaalgemeten, een relatief lage vloeispanning met significante rekversteviging.

Er zijn dus twee afwijkingen van het algemene macroscopisch materiaal gedrag gemeten. Teneerste een afname in ductiliteit bij toenemende korrelgrootte voor de experimenten op Al folie.Ten tweede een combinatie van een hoge vloeispanning en ductiliteit voor materiaal met eenultrafijne microstructuur.

Chapter 1

Introduction

In the electronic industry miniaturisation is an important topic, as products (such as mobilephones, walk-mans etc.) become smaller and smaller. With the decreasing size of these prod-ucts the components and parts have to be smaller as well. A level has been reached at whichthe material behaviour may be different than the macroscopic behaviour. For example it mayno longer be arbitrarily that the flow stress decreases or the ductility increases with increasinggrain size.

Due to this miniaturisation the material behaviour at this small scale has to be investigated.The microstructure will play an important role, where so-called size-effects will occur. The ma-terial cannot be considered homogeneous anymore, the separate grains (size and orientation)will determine the mechanical properties more and more.

The goal of this project is firstly, to investigate the importance of grain size effects in micro-forming. Sheets with a varying ratio (

� �) between thickness and grain size have been analysed

and their behaviour is investigated by tensile, punching and drawing experiments typical forforming processes in industry.

Secondly, the material behaviour of samples with an ultra fine grain structure has been in-vestigated. The development of such material has advantages for structural applications withimproved mechanical properties of higher yield strength and superplasticity. Several severeplastic deformation exist methods, which can be used to make ultra fine grained material; inparticular equal channel angular extrusion, accumulative roll bonding, cyclic extrusion com-pression and multi axial compression.In this project multi axial compression is used to produce ultra fine grained samples. With thissevere plastic deformation method deformation levels higher than a true strain of 10 can easilybe achieved. This compression technique makes it possible to obtain grain sizes in the micronor sub-micron range. The mechanical properties of these material were unknown and havebeen measured through micro-hardness and uniaxial compression tests.

This thesis is organised as followed, it consists of two parts: (1) investigations on size-effectsin micro-forming of foil and (2) experiments on material processed by multi axial compres-sion. But first some theoretical considerations and a literature review are presented in the nextchapter.

Chapter 2

Theoretical considerations

Basic theory on deformation mechanisms is reviewed. Thereafter an overview is given onobservations of grain size-effects and specifically results for tensile and punching experiments.For drawing of thin metal sheets, nothing could be found in literature related to size-effects.

2.1 Plastic deformation

The basic component of a metal is an atom, the way these atoms are packed determines thekind of crystal structure. This structure can be subdivided in repetitive parts, the so-calledunit cells. The three most common structures for metals are face-centered cubic (FCC), body-centered cubic (BCC) and hexagonal close packed (HCP), the two cubic unit cells are shownin figure 2.1. A set of these unit cells with a specific orientation is a grain. Because for thisinvestigation only aluminium and aluminium alloys are used (chapter 3), only the propertiesof the FCC structure will be discussed.

Figure 2.1: BCC and FCC unit cells

Dislocations and slipPlastic deformation is carried by the movement of so-called dislocations through thematerial on the so-called slip planes. Formally, a dislocation is a line defect separatingthose regions on the slip plane which have undergone slip from those that have notyet.Dislocations are linear distortions in a crystal lattice, the two basic types are shownin figure 2.2. An edge dislocation can be considered as an extra half-plane of atomswithin the crystal. The screw dislocation derives its name from the spiral path or rampthat may be traced around the dislocation line by the atomic planes of atoms.

Chapter 2 Theoretical considerations 3

Figure 2.2: (a) Edge dislocation (b) Screw dislocation

The extent of slip of one part of the crystal relative to the other is determined by the so-called Burgers vector. The atoms that were formerly nearest neighbours are displacedby a lattice translation vector: the Burgers vector [1]. The Burgers vector for a FCClattice is:

�� (2.1)

In the vicinity of a dislocation compressive, tensile and shear strains are imposed onthe neighbouring atoms. The elastic energy associated with the dislocations is �� ,(b = length of the Burgers vector), so if two dislocations of equal sign lie next to eachother their energy will increase. The length increases from

�to 2

�, and the energy in-

creases a factor 4. This is more than the energy for two separate dislocations and thusthe dislocations will feel a repulsive force. On the other hand if two dislocations withopposite sign meet they may annihilate and the elastic energy is released.Dislocations do not move along all planes of atoms in each crystallographic directionwith the same ease, the energy needed for breaking and establishing interatomic bondsis decisive. The slip plane and the Burgers vector are called the ”slip system”. The slipplane is the plane with the densest atomic packing and the slip direction the directionwith the highest linear density. For the FCC lattice these slip systems are the �� directions and � �� planes.

Stacking faultsUp to now only ’perfect’ dislocations have been discussed. However perfect disloca-tion may dissociate into partial dislocations. The Burgers vector associated with thesepartial dislocations is not a translation of the perfect lattice. As a consequence thesepartial dislocations lead to stacking faults. These stacking faults can also arise duringcrystal growth in (re-)crystallisation processes. The relevant Burgers vectors, for theFCC lattice, associated with the presence of partial dislocations are depicted schemati-cally in figure 2.3 and may be associated with a reaction of the type [1]:

� �� !"� � �#�%$ � �!&�� (2.2)

Sliding the upper half-space with respect to the lower half-space by a vector connect-ing the B sites to the C sites ( ')(* � � �#� ), the perfect ABC stacking sequence is disrupted,resulting in an ABCBCABC stacking. These stacking faults result in a certain energypenalty, the stacking fault energy.


Figure 2.3: (a) Sketch of slip plane region of a crystal with an edge dislocation, the full Burgers vectorb is decomposed into two smaller vectors �� and �� (b) Pile-up of dislocations at a grainboundary

Dislocations and grain boundariesDislocations move through the material during plastic deformation. During these glid-ing motions the dislocations can impinge on a grain boundary, which acts as an obsta-cle. The dislocations pile-up at the grain boundaries (figure 2.3). This pile-up can resultin processes within the grain boundary itself or on the other hand it can result in thedevelopment of plastic deformation in the adjacent grain. Increasing the amount ofgrain boundaries through grain size reduction will increase the stress necessary to de-form the material, because there are more barriers which hinder the movement of thedislocations.

For various metals a relationship can be found being the so-called Hall-Petch relation.

�� $� �� (2.3)

The flow stress and grains size are related as is shown in equation 2.3, �� . ThisHall-Petch behaviour is found for several metals. One explanation is that pile-up at agrain boundary in one grain can generate sufficient large stresses to operate sources inan adjacent grain at the yield stress.

Dislocations and hardeningHardening is caused by the pile-up of dislocations at barriers in the material. Thesebarriers are among others dislocations, grain boundaries and second phase particles.Dislocation motion through the material becomes more difficult, increasing the amountof obstacles where dislocations are pinned.

General material behaviourThe above mentioned effects lead to behaviour that can be generalised as follows. Intension the flow stress and ductility are usually related as shown in figure 2.4.a, if thematerial has a high flow stress the ductility will be poor and vice versa. Increasingthe grain size generally leads to a decrease of the flow stress and an increase of theductility. Both effects can be attributed to the decreasing amount of grain boundaryarea with increasing grain size. The decrease of grain boundaries decreases number of


barriers which hinder migration of dislocations. Hence the mobility of the dislocationsincreases and consequently the material becomes softer and more ductile.

Figure 2.4: (a) Schematic diagram of the relation between flow stress and ductility (b) Schematic ofstress-strain curves for pure and alloyed Al. (eq. Al-Mg)

In figure 2.4.b the material behaviour for pure Al and an alloy is schematically repre-sented, the pure Al shows almost no strain hardening. This can be associated with theso-called dynamic recovery. Because Al has a high stacking fault energy, the numberof partial dislocations will be small and there are only ’perfect’ dislocations. Duringthe plastic deformation the screw dislocations will migrate through the material andcan change their slip plane through cross-slip. Cross-slip may lead to annihilation ofscrew dislocations, and part of the strain hardening effect is lost. The edge dislocationscannot readily leave their slip plane and instead reorganize into a network structure.Alloying elements may lower the stacking fault energy and reduce the likelihood ofcross-slip. Hardening will therefore be more prominent.

2.2 Size-effects in tension

Flow stress

Kals et al. [3] have shown that there is a decrease in flow stress with increasing frac-tion of surface grains for Cu alloys. The flow stress reduces with decreasing specimenthickness � � or

�. This is shown in figure 2.5.

Kals et al. state that this decrease in flow stress is caused by the higher number of ac-tive slip systems in surface grains. Thus an increase of the fraction of surface grains,by decreasing the specimens size, will lead to a decrease in flow stress.

Nakamachi et al. [4] present uniaxial tensile results of an aluminium alloy (Al-2.5 �Mg, A5052), using specimens with grain sizes of 10 �� to 3000 �� . The samples are5x15x0.25 �� rectangular sheets. The results of these tests are shown in figure 2.6. Ob-viously, the flow stress increases with decreasing grain size. This can be associatedwith two effects: the decreasing fraction of surface grains (explained above) and theincrease of total grain boundary area.


Figure 2.5: Flow stress of CuNi18Zn20 at different true strain for different length scales ( � ) [from Kals et al.]

Figure 2.6: Tensile test results by Nakamachi et al. for different grain sizes at constant specimen size

Ductility

The grain size of the material is also important in determining the ductility of the ma-terial. From a macroscopic point of view (relatively large samples, with small grains)the ductility increases when the grain size increases. Again this can be explained bythe specific grain boundary area, it decreases with increasing grain size. However thisseems not to be the case at the micro-forming scale.

Nakamachi et al. [4] find, as shown in figure 2.6, a decrease in ductility with increasinggrain size. This effect is also found by Kals et al. [3], these results are shown in figure2.7.

This decrease in ductility is explained by the increasing importance of the properties ofsingle grains upon miniaturisation. The weakest grain will determine the mechanicalproperties more and more. Having only one grain over the sample thickness but stillmany across the length and width, the properties of the weakest grain is not averagedanymore by the others. The deformation will concentrate on this weak part, and thematerial will fracture earlier. Thus miniaturisation leads to a stronger localisation ofthe processes of necking and fracture.


Figure 2.7: Percentage necking elongation �� for different values of the length scale (thickness) � and grain size�[from Kals et al.]

2.3 Size-effects in punching

Kals et al. also investigated the effect of miniaturisation for punching tests (figure 2.8).

Figure 2.8: Ultimate shear strength �� versus length scale

The maximum shear strength remains almost constant with miniaturization when thegrain size is held constant. Enlarging the grain size causes an obvious decrease in shearstrength, but this decrease diminishes with decreasing specimen size. This behaviourcannot be explained on the basis the results of the tensile tests. In punching thereare kinematic constraints which determine that the deformation is imposed at specificpoints or grains. The material in the deformation zone is restrained by the surroundingmaterial as well as the punch and die. This means that the fraction of surface grains,that contribute to the decrease in flow stress, does not take effect in punching. En-largement of the grain size however leads to a significant decrease in maximum shearstrength, because a diminishing number of grains, in the specimen cross-section, cancontribute to the cushioning of the imposed deformation.Miniaturization also leads to an increasingly irregular development of the shearededge, where the orientation of the single grains towards the shearing direction seemsto become decisive [3].


Figure 2.9: Punch load against punch displacement

Raulea et al. [5] performed punching tests on poly-crystalline and single crystal alu-minium. The results are shown in figure 2.9, it shows that there is a loss of reproducibil-ity for the single crystal specimens. The differences in the deformation behaviour iscaused by the different grain orientations in the blanking specimens.

Chapter 3

Micro-forming of Al foils

In this chapter the first part of this project is presented, grain-size effects in micro-forming.

3.1 Materials

To investigate grain size-effects it is advantageous to select materials for which a solidbasis exists on their physical, chemical and mechanical properties. Three criteria arelisted below which the chosen material should meet.

� The reference material needs to be pure to avoid complications due to the sec-ond phase particles. Pure metals of technical quality may pose problems as well.For example, most ’pure’ Al that is commercially available contains iron (Fe) andsilicon (Si) as impurities.

� The material should be FCC. This is a particular limitation in this work. The slipsystems for FCC metals are well defined and a lot is known about their deforma-tion.

� A high stacking fault energy is preferred because this hampers the formation oftwins and cross-slip of dislocations. The absence of twins gives a simpler mi-crostructure, and no cross-slip makes the analysis of the deformation easier.

Aluminium meets these criteria. For this research two aluminium types were chosen,pure Al plates and commercial Al foil.

Pure Al, the reference materialAl plates, with a purity of 99.999 � , were rolled to obtain sheets with a thickness of230 �� to 340 �� (table B.1, appendix B). Before processing this material is annealedat 580 � �

for 1 hour.

Commercial Al foilBefore doing the experiments on the pure Al, the experimental set-ups have been testedusing aluminium foil, with a thickness of 100 �� . Because many data has been gath-ered with this material, as a possible industrial material, it will also be used to investi-gate size-effects. This Al has a purity of 99.5 � and further contains of iron, silicon and

Chapter 3 Micro-forming of Al foils 10

calcium, nickel and zinc are only measured in intermetallic phases. The compositionof this material, as determined with EDX, and is shown in table 3.1.

Table 3.1: Chemical composition of the commercial Al foil

Element Al Fe Si Ca Ni Znwt � 99.5 0.28 0.1 0.13 - -

The experimental set-up was tested using the as-received foil, with an average grainsize of about 1.9 �� as can be seen in figure 3.1. The grain size has been determinedusing the mean linear intercept method. To make the grains visible the specimen is me-chanically polished in several steps up to 1 �� and subsequently electro-polished on aStruers Lectropol (see also appendix A). The images are taken with an environmentalscanning electron microscope (esem). In order to be able to distinguish between thegrains a backscatter electron detector is mounted. The small particles in the images areFe and Si rich phases, the exact chemical composition could not be determined becausethe particles are to small.

Figure 3.1: Microstructure of the as-received foil


3.2 Sample preparation

The most common way to obtain different grain sizes is to deform the material plasti-cally and apply a heat-treatment. Here the deformation is imposed by rolling and thematerial is heat-treated at several temperatures, ranging from 100 � �

to 600 � �.

3.2.1 Rolling

Conventional rolling is used to make aluminium sheets from 1 �� thick plates. Theplates are cut into strips of 150x30x1 �� . After grinding the cutting edges these stripsare rolled. The resulting thickness is about 230 �� and for tensile testing an additionalset is rolled to 340 �� . The rolling procedure can be found in appendix B.

Figure 3.2: Microstructure of pure aluminium after rolling, thickness reduction of 77 � (sample set S1)

As can be seen in figures 3.2 and 3.3 the microstructures after rolling are very differentalthough the final sheet thickness is almost the same. In figure 3.2 a homogeneousgrain structure (89 �� ) can be observed, but in figure 3.3 there are very small grains inthe order of a few microns (3.2 �� ) with random distributed large grains (100-500 �� ).The reason for this might be that the microstructure of the strips before the rolling wasdifferent, unfortunately it has not been possible to verify this.

Figure 3.3: Microstructure of pure aluminium after rolling , thickness reduction of 77 � (sample set S3)


3.2.2 Recrystallisation

Before starting the recrystallisation treatment, samples of 35x5 �� are cut from therolled strips. The cutting edges are ground till 3 �� resulting in a sample width ofabout 4.2 �� . This is done before the heat-treatments, because afterwards the alu-minium sheets will be softer and therefore more difficult to machine. These samplesare used in all experiments, only the thickness ( � ) of the sheets may vary. A schemati-cally representation of the samples is given in figure 3.4.

Figure 3.4: Schematic of samples used for tensile, punching and drawing experiments

The recrystallisation process is governed by two factors, nucleation and grain growth.The driving force is the decrease of internal energy through the decrease of the totalgrain boundary area and reduction of strain energy related to dislocations .At a tem-perature near the melting temperature of the material nucleation will be small, becausethe temperature difference is too small to supply the necessary activation energy forthe formation of new nuclei. On the other hand the grain growth rate will be higher atelevated temperatures. Therefore a larger grain size is obtained at elevated tempera-tures, since only a few nuclei will be formed, which will grow rather fast.

Table 3.2: Recrystallisation treatments for the pure tensile specimens (std=standard deviation)

Set Heat-Treatment Grain size (std) [ �� ] Set Heat-Treatment Grain size (std) [ �� ]S1 1h 250 � � 85 (31) S1 1h 580 � � 446 (174)S1 0.5h 393 � � 192 (45) - - -S2 1h 100 � � 52 (25) S2 0.5h 385 � � 302 (80)S2 1h 255 � � 107 (35) S2 1h 580 � � 417 (124)S5 0.5h 254 � � 3.1 (0.8) S5 1h 587 � � 870 (290)

Pure Al

Tensile specimensTensile experiments have been done on sheets with t = 340 �� and t = 230 �� . Both setshave been heat-treated to obtain different microstructures by recrystallisation. How-ever it has not been possible to obtain the same set of grain sizes for all sample sets,


because of the differences in the microstructure after rolling. The differences in grainsize for samples heat-treated at the same temperature can possibly also be attributedto the differences in prior deformation history. In table 3.2 the recrystallisation treat-ments can be found, the resulting grain sizes are in the range of 3 to 870 �� . The setS5 (340 �� ) was recrystallised in the temperature range of 300-400 � �

. However thegrain sizes are in the same range as for the set from S5 heat-treated at 587 � �

. Thesesamples have not been used in the further analysis. In figures 3.5 and 3.6 some typicalmicrostructures are shown, images of the other samples can be found in appendix B.

Figure 3.5: (a) Mean grain size of 52 �� (S2) (b) Mean grain size of 192 �� (S1)

Figure 3.6: (a) Mean grain size of 446 �� (S1) (b) Mean grain size of 870 �� (S5)

Punching and drawing specimensThe obtained grain sizes for the punching samples leave a wide range open (table 3.3,S3). Again the heat-treatments at about 390 and 580 � �

, resulted in the same grain size,in this case 700 �� . This can be probably attributed to the microstructure after rolling,where set S3 also showed a dual grain size similar to set S5 (figure 3.3, appendix B).So for the punching the behaviour of only 3 sets is measured, the as-deformed, shortheat-treated and the fully annealed one.


Table 3.3: Recrystallisation treatments for the pure punching and drawing specimens (std=standard deviation)

Set Heat-Treatment Grain size (std) [ �� ] Set Heat-Treatment Grain size (std) [ �� ]S3 0.5h 250 � � 442 (182) S6 0.5h 250 � � 160 (91)S3 1h 575 � � 712 (220) S6 0.5h 392 � � 300 (75)- - - S6 1h 577 � � 531 (142)

Set S6 is used to investigate grain size-effects in drawing. Even though a dual mi-crostructure is present after rolling, it has been possible to obtain a good grain sizerange. Images of the microstructures are shown in appendix B.

Commercial Al foil

In figures 3.7 and 3.8 the four obtained recrystallised microstructures are shown. Thesamples have been recrystallised at temperatures ranging from 143 � �

to 550 � �. The

mean grain sizes are 1.8, 3.3, 38, and 70.5 �� respectively.

Figure 3.7: (a) Mean grain size of 1.8 �� (2) (b) Mean grain size of 3.3 �� (3)

Figure 3.8: (a) Mean grain size of 38 �� (4) (b) Mean grain size of 70.5 �� (5)


Figure 3.7.b shows a dual grain structure, small grains with random distributed largerones having a size of 20-50 �� . This microstructure is achieved with a very ’exotic’heat-treatment as shown in table 3.4. Probably the last stage on this treatment initiatedthe recrystallisation, but it may have been too short to obtain a homogeneous structure.

Table 3.4: Recrystallisation treatments for the Al foil specimens (std=standard deviation)Set Heat-Treatment Grain size (std) [ �� ]1 1h 143 � � 1.8 (0.7)2 4h 143 � � + 4x1h 143 �� + 0.25h 174 �� 3.3 (1.4)3 0.5h 352 �� 38 (12.4)4 1h 550 � � 70.5 (18.7)

3.3 Mechanical behaviour

Tensile, punching and drawing experiments have been conducted to investigate thesize-effects. These tests have been performed on a microtest device from Deben. Onthe traverses of this tensile stage different modules can be mounted for particular testset-ups. A schematical representation of the microtest device is shown in figure 3.9.The device has a size of about 135x85x40 �� . The microtest stage is equipped with a690 � loadcell and can be used under an optical microscope as well as in a scanningelectron microscope.

Microtest stage

Punching / Drawing(Compression)

Tensile tests(Tension)

Figure 3.9: Microtest device with tensile, punching and drawing modules

3.3.1 Tensile experiments

To investigate the effect of a particular (grain size related) microstructure on the ma-terial behaviour tensile test have been done. With these test the effects on flow stress,


tensile strength and the strain at fracture can be found. First the results for the pure Alare presented. To be able to compare the obtained data from the tensile experiments,� �

is introduced as the ratio of the specimen thickness and the average grain size.

Pure Al

In figure 3.10 the results are shown for the pure Al samples with a thickness of about340 �� . The tensile curves for three samples of each set have been measured. Only themean tensile curves are shown because the good reproducibility of the measurements,the curves are plotted up to the mean fracture strain. The true stress is calculated underthe assumption of volume invariance and �� is used to calculate the true strain. Theflow stress is measured using the 0.2 � strain offset method, the flow stress and strainat fracture are presented in table B.1.

0 0.05 0.1 0.15 0.2 0.25 0.30

10

20

30

40

50

60S5

true strain [−]

true

str

ess

[MP

a]

as−deformed1h 587 C0.5h 254 C

d = 3.2 µm, λt = 106

d = 3.1µm, λt = 110

d = 870 µm, λt = 0.4

Figure 3.10: Mean tensile curves of S5 tensile sheets

The results show that the flow stress decreases and the ductility increases with increa-sing grain size. These two effects of an increasing grain size reflect the well-knownmaterial behaviour at the ’macroscopic’ level. Both can be attributed to the decreasingamount of grain boundary area with increasing grain size. As mentioned before thedecrease of grain boundaries decreases the barriers which hinder dislocation move-ment. Thus the mobility of the dislocations increases, the material becomes softer andmore ductile. The decrease in flow stress is also caused by the increasing ratio of grainsin the surface region. These grains can deform easier because they have a free surface,there are no constraints against the deformation in that direction.

Table 3.5: Flow stress and strain at fracture of S5 (std=standard deviation)Set Grain size[ �� ] Flow stress (std) [ �� ] Strain at fracture [-]

as-deformed 3.2 47.2 (1.6) 0.040.5h 254 �� 3.1 42.3 (5.5) 0.041h 587 �� 870 7.1 (1.7) 0.28

Tensile experiments are also done on samples with a thickness of about 230 �� . Theresults for two sample sets are presented in figure 3.11, again three samples of each set


have been measured. The results for these tensile tests show the same trend for theflow stress as above, it decreases with increasing grain size (table 3.6). However forthese experiments a decrease in ductility can be observed with increasing grain size.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.350

10

20

30

40

50

60

70S1

true strain [−]

true

str

ess

[MP

a]

0.5h 385 C1h 580 C1h 250 Cas−deformed

d = 89 µm, λt = 2.6

d = 85 µm, λt = 2.7

d = 192 µm, λt = 1.2

d = 446 µm, λt = 0.5

0 0.05 0.1 0.15 0.2 0.25 0.3 0.350

10

20

30

40

50

60

70S2

true strain [−]

true

str

ess

[MP

a]

1h 255 C1h 580C0.5h 385 C1h 100 C

d = 52 µm, λt = 4

d = 107 µm, λt = 2

d = 302 µm, λt = 0.7

d= 417 µm, λt = 0.5

Figure 3.11: (a) Results for set S1(b) Results for set S2

For sample set S1 the ductility increases first, from the as-deformed state to the oneheat-treated for 1 hour at 250 � �

. Although the grain size of both sets is almost equal,there is an increase in ductility, resulting from recovery. During this recovery the in-ternal energy of the as-deformed samples decreases and hence the amount of disloca-tions will decrease. As stated in chapter 2, dislocations interact with their neighbours,which restricts their mobility. Therefore the ductility of the material will increase if theamount of dislocations decreases, there are less barriers against plastic deformation.

Table 3.6: Flow stress and strain at fracture of S1 and S2 (std=standard deviation)Set Grain size[ �� ] Flow stress (std) [ � � ] Strain at fracture [-]

S1: as-deformed 89 24.8 (1.5) 0.27S1: 1h 250 � � 85 12.8 (1.8) 0.31

S1: 0.5h 393 � � 192 12.2 (2.3) 0.27S1: 1h 580 � � 446 9.1 (0.3) 0.25S2: 1h 100 � � 52 15.7 (1.4) 0.29S2: 1h 255 � � 107 11.4 (1.2) 0.32

S2: 0.5h 385 � � 302 7.4 (0.9) 0.24S2: 1h 580 � � 417 8.6 (1.4) 0.23

However from this point the ductility decreases with increasing grain size, althoughthe total grain boundary area decreases and dislocations can move easier. This can beexplained by the increasing influence of the weakest grain on the material behaviour,the properties of this grain are not averaged anymore by the surrounding ones (in thethickness direction). Therefore the deformation will concentrate on this weak part, andfracture will occur at lower strain levels. This behaviour is also found for the secondset (S2) and in literature ([2],[4]).


In figure 3.12.a the flow stress in plotted against� �

for the heat-treated samples. As canbe seen the flow stress decreases with decreasing

� �. As discussed above this is due to

the change in total grain boundary area with decreasing grain size and might also becaused by the surface effect.

0 1 2 3 4 50

2

4

6

8

10

12

14

16

λt [−]

flow

str

ess

[MP

a]

S5S1S3

0 1 2 3 4 50

2

4

6

8

10

12

14

16

d−1/2 [mm−1/2]

flow

str

ess

[MP

a]

Figure 3.12: (a) Flow stress against � � (b) Hall-Petch behaviour of pure Al

In figure 3.12.b the flow stress ( � � ) of all recrystallised samples is plotted against thereciprocal of the square root of the grain size ( ). Within the margins of the experimen-tal errors the materials behave according to a Hall-Petch relation. Effects of the surfaceon the yield strength cannot be observed.

Al foil

In figure 3.13.a the mean curves are shown of the tensile experiments for the 100 ��thick Al foil with 5 different microstructures. The tensile properties of 5 samples ofeach set have been measured.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.350

20

40

60

80

100

120

140

160

180

true strain [−]

true

str

ess

[MP

a]

d = 1.9 µm, λt = 52.6

d = 1.8 µm, λt = 55.6

d = 3.3 µm, λt = 30.3

d = 70 µm, λt = 1.4

d = 38 µm, λt = 2.6

0 5 10 15 20 250

25

50

75

100

125

150

d−1/2 [mm−1/2]

flow

str

ess

[MP

a]

Figure 3.13: (a) Mean tensile curves of Al foil experiments (b) Hall-Petch behaviour of Al foil

The material behaviour is comparable to that of the pure Al samples. It shows thatwith increasing grain size the flow stress decreases and the ductility increases at first(appendix C). This decrease in flow stress is explained, as mentioned above, by the


decreasing number of grain boundaries with increasing grain size. These grain bound-aries are barriers against dislocation movement, so the dislocations can move easierthrough the material. When the grain size grows above 38 �� a decrease in the duc-tility can be observed, as stated above this is due to the increasing importance of theweakest grain on the material behaviour.

3.3.2 Punching

The punching experiments have also been done on the microtest device, punchingmodules (die and punch holder) are mounted on the load cell and the traverse. Theseare shown in figure 3.14, in the design of the modules it is taken into account that thepunching process has to be visualised under a microscope. Therefore the two clampsare situated at the bottom of the die holder, the die has a width of 4.04 �� and thepunch-width is 4 �� , hence the die-punch clearance is 40 �� .

Figure 3.14: Schematic of punching modules; die holder, punch holder , clamps and the punch and die

Pure Al

Three samples from each set have been tested, the as-deformed sheets and sheets witha grain size of 442 �� and 712 �� . The thickness of the Al specimen is about 230 �� .In figure 3.15 and table 3.7 the punching results are shown, with increasing grain sizethree effects can be observed:

� The maximum shear strength decreases with increasing grain size.� The reproducibility of the maximum shear strength deteriorates with increasing

grain size.� The punch displacement at the maximum shear strength shows an initial increase

followed by a decrease.

As already mentioned for the tensile results, the number of grain boundaries decreaseswhen the grain size is increased. These grain boundaries act as barriers which hin-der the movement of the dislocations. The material can be deformed more easily and


0 0.1 0.2 0.3 0.4 0.50

10

20

30

40

50

60

70

punch displacement [mm]

shea

r st

ress

[MP

a]

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40

10

20

30

40

50

60

70


shea

r st

ress

[MP

a]

as−deformed0.5h 250 C1h 575 C

d = 2.9 µm, λt = 79 d = 442 µm, λ

t = 0.5

d = 712 µm, λt = 0.3

Figure 3.15: (a) Punching curves for pure Al sheets (b) Mean punching curves and maximum shearstrength

the maximum shear strength decreases. As can be seen in figure 3.15.b the decreasein shear strength diminishes with increasing grain size, there is only a small changebetween the two heat-treated sets.In contradiction to the tensile experiments, punching is a non-homogeneous test method,there are kinematic constraints resulting from the deformation. The type and positionof the applied deformation is determined by the experimental set-up. The stretch-ing and shearing of the material occurs in the clearance between punch and die. Forthis reason the deviation between the measurements of the same set will increase withincreasing grain size. The orientations of the grains in the deformation zone deter-mine the material behaviour, the other grains have negligible influence. At increasinggrain size the amount of grains, having different orientations, in the deformation zonedecreases. Therefore the samples (although from the same set) can show a differentmaterial behaviour, because the grains in the deformed zone had different (’average’)orientations.

Table 3.7: Shear strength and punch displacement at maximum shear stress (std=standard deviation)Set Grain size[ �� ] Shear strength (std) [ �� ] Punch displacement [mm]

as-deformed 2.9 64.8 (0.4) 0.180.5h 250 � � 442 50.6 (1.1) 0.271h 575 � � 712 47.1 (2.8) 0.23

For the tensile experiments a decrease in ductility could be observed, here the punchdisplacement at the maximum shear strength shows the same trend. Comparing theas-rolled results with the results for the 442 �� sheets, there is an increase in displace-ment. However between the two recrystallised sets the punch displacement decreases,which is in agreement with the change in ductility for the tensile tests.


Al foil

In figure 3.16 the punching results for the commercial Al foil are shown. The strongerdeviation at increasing grain size ,between the measurements of the same set, is notobserved for these experiments. There are still a lot of grains present in the deformationzones compared to the pure Al samples.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.350

10

20

30

40

50

60

70

80

90

100


shea

r st

ress

[MP

a]

as−received1h 143 Cset 2 0.5 h 400 C

d = 1.9 µm, λt =52.6 d = 1.8 µm, λ

t = 55.6

d = 3.3 µm, λt = 30.3

d = 38 µm, λt = 2.6

0 10 20 30 40 50 6050

55

60

65

70

75

80

85

90

95

100

λt [−]

shea

r st

reng

th [M

Pa]

Figure 3.16: (a) Mean punching curves for Al foil (b) Maximum shear strength

The shear strength decreases with increasing grain size, as has been observed for thepure Al sheets. For the three strongest materials the differences are also due to thedecreasing number of dislocations in the material. The heat-treatments lead to morerecovery than recrystallisation. Decreasing the number of dislocations in the materialincreases the mobility of the remaining dislocations. There is a smaller amount of dis-locations that interact.As can be seen in figure 3.16.a the punch displacement at the maximum shear stress in-creases with increasing grain size. A decrease in punch displacement after the increase,as seen for the pure Al sheets, is not observed here because samples with a larger grainsize have not been tested.

3.3.3 Drawing

Drawing experiments have only been done on the pure Al sheets with a thickness ofabout 260 �� . Results are shown in figure 3.17. The punch width is 3 �� and the diewidth is 3.5 �� , the punch and die edges are rounded with a radius of 0.35 �� .

Table 3.8: mean maximum force (std=standard deviation)Set Grain size[ �� ] Maximum force (std) [

�]

as-deformed 4.6 99.2 (3.8)2 160 97.0 (7.6)3 300 78.2 (4.3)4 531 85.2 (9.0)

The drawing curves show a stronger deviation with increasing grain size, as can beseen in figure 3.17.a. In table 3.8 this is shown through the increase of the standard de-


viation for the maximum punching force. As for the punching, the deformation zoneis determined by the experimental set-up. At increasing grain size the ’mean’ orienta-tion of the grains in this zone will vary more and more between the samples of each set.

0 0.5 1 1.50

10

20

30

40

50

60

70

80

90

100

110


punc

hing

forc

e [N

]

0 0.2 0.4 0.6 0.8 1 1.2 1.40

10

20

30

40

50

60

70

80

90

100

110


punc

hing

forc

e [N

]

d = 160 µm, λt = 1.6

d = 300 µm, λt = 1.1

d = 531 µm, λt = 0.5

d = 4.6 µm, λt =56.5

Figure 3.17: (a) Drawing curves (b) Mean drawing curves

The maximum punching force decreases with increasing grain size, but the decreasediminishes as the grain size is increased more. The change in maximum force for set2 and 3 is considerable, but for set 3 and 4 the change is probably not significant. Thisbehaviour has also been observed for the punching experiments.

3.4 Conclusions

Tensile testingThe obtained results show that a changing grain size has a large effect on the mate-rial properties measured in tensile experiments, grain size-effects do occur. The flowstress decreases with increasing grain size, there are less constraints against deforma-tion, the materials seem to behave according to the Hall-Petch behaviour. The ductilityincreases at first with increasing grain size, but if the grain size has reached a certainlevel this increase changes in a decrease. From experiments on the Al sheets and foilit seems that this decrease occurs when

� �is about 3. As said this decrease in ductility

can be explained by the increasing importance of the properties of the weakest grain.

PunchingThe shear strength decreases with increasing grain size, this effect can be attributed tothe decrease in total grain boundary area. There are less constraints against dislocationmovement, the material becomes weaker. However the decrease in strength dimin-ishes with further increase of the grain size. The deviation of the measurements of themaximum shear strength increases with increasing grain size, because the ’average’orientation in the deformation zone varies stronger per sample with increasing grainsize. Increasing the grain size also leads to an increase in punch displacement for themaximum shear stress, but the displacement decreases as the grain size increase con-tinues.


DrawingAn increase in grain size leads to a stronger deviation in the measurements, the spe-cific orientations of the decreasing number of grains in the deformation zone play anincreasing role. At increasing grain size the probability of a varying ’mean’ orientationfor samples from the same set increases. Increasing the grain size also initially leadsto a decrease in the maximum punching force, but this decrease diminishes upon acontinued increase in grain size.

Chapter 4

Multi Axial Compression

In this chapter the second part of the investigation on grain size-effects is presented.First the multi axial compression (MAC) technique is presented. The MAC has beendone at the Technical University of Delft on a Maxstrain unit (figure 4.1) connected toa Gleeble 3500 system manufactured by DSI.

Stroke

Wedge

Sampleholder

Sample

Sampleholder

Figure 4.1: Chamber of the Maxstrain unit

As can be seen in figure 4.1 the sample is clamped between the stroke and wedge.The sample is first compressed in one direction. After the stroke and the wedge arewithdrawn, the sample is turned 90 degrees, followed by compression in this newdirection. The process is repeated until the predetermined deformation level (numberof hits ( � )) has been reached.

��

�� $ � � �� $ �� $ � � (4.1)

Depending on the material, deformation levels up to a true strain of 30 can be applied.The total amount of true strain ( �� ) can be calculated by equation 4.1, this equation isobtained from the best-fit on data of experiments with a thickness reduction of 50 � inthe first hit ( � � � � �� ) [6]. Therefore the total amount of strain can only be calculated ifthe processing conditions are equal.

Chapter 4 Multi Axial Compression 25

4.1 Sample preparation

Two Al alloys are processed with MAC, being LN1 and Al 51st. After the deformationand heat-treatments the mechanical behaviour of these two materials are measured,which will be presented in the next section. First the processing and recrystallisationof the two alloys will be discussed, starting with the LN1 alloy.

4.1.1 LN1

At the university of Delft some work has been done by Gholinia et al. [6] on the pos-sibilities of this technique (MAC) to produce ultra fine grained aluminium. One of thematerials used in this investigation is the alloy LN1 (table 4.1). Gholinia et al. have notbeen able to determine the mechanical properties of the materials.

Table 4.1: Chemical composition of LN1

Element Al Si Fe Mn Mgwt � - 0.2 0.36 0.14 1.02

To provide us a reference and to make and to complete the research done in Delft,it is chosen to use the LN1 alloy. The specimens, with a size of 430x10x10 �� , areprocessed up to a deformation level of a total true strain of 26.5 (equation 4.1). Thethickness reduction in the first hit is 50 % and the number of total hits to achieve thedeformation level is 30. The gap between the stroke and the wedge is 5 �� for each hit.

Figure 4.2: (a) LN1 alloy after deformation (b) LN1 alloy after deformation processed by Gholinia et. al

In figure 4.2 the microstructure after deformation of the Al is shown, in the right aelectron backscatter pattern (EBSP) from Gholinia’s sample is shown. As can be seenthe obtained microstructures both show a submicron grain size, the mean grain sizefor Gholinia’s samples is 0.2 �� and 1 �� for our samples. The higher mean grain sizefor our samples can partly be attributed to the used grain size measurement method,the mean linear intercept method. This is a linear analysis method and not an areameasurement as used by Gholinia et al..


Compression and Vickers hardness measurement results will be discussed in the nextsection. For these experiments some specimens have been heat-treated, one set for 1hour at 248 � �

another set for 2 hours at 480 � �. The microstructures of these two

sets are shown in figure 4.3, the obtained grain sizes are 1.8 �� and 26 �� respec-tively. The small particles are Mg and Si rich phases, the exact composition could notbe determined because the particles are very small.

Figure 4.3: (a) LN1 alloy set A2 (b) LN1 alloy set A3

Because the deformed samples are severely damaged, the procedure has been altered.The compression in the first hit is changed into a thickness reduction of 40 %, hencethe gap between stroke and wedge is 6 �� . The number of hits is not changed (30).This procedure results in a more reproducible sample geometry after deformation. Thegrain size after compression is 1.14 �� and for the heat-treated samples 1.9 �� and 29�� (Set B table 4.2, appendix D).

Table 4.2: Heat-treatments and recrystallisation of LN1 alloy

Set Heat-Treatment Grain size (std) [ �� ] Set Heat-Treatment Grain size (std) [ �� ]A1 - 0.96 (0.47) B1 - 1.14 (0.28)A2 1h 248 � � 1.8 (0.5) B2 1h 248 � � 1.9 (0.6)A3 2h 480 �� 26 (4.8) B3 2h 480 � � 29 (9.2)

4.1.2 Al 51st heat-treated

The second alloy that has been processed with this severe deformation technique is Al51st, its composition is shown in table 4.3.

Table 4.3: Chemical composition of Al 51st

Element Al Si Mg Mn Cr Znwt � - 1 0.9 0.7 0.15 0.1


The as-received material was too strong and brittle to be able to apply a high defor-mation level, therefore the material has been heat-treated. Now the samples can besubjected to 10 hits with a thickness reduction of 40 % in the first hit. The microstruc-ture of the heat-treated and deformed Al can be seen in figure 4.4, the small particlesare as for the LN1 alloy Si and Mg rich phases.

Figure 4.4: (a) Microstructure of Al 51st after heat-treatment (b) Microstructure after plastic deformation

As can be seen in the images the grain size before the severe plastic deformation isin the 200-500 �� range, after deformation the grain size has been reduced to 0.9 �� .These deformed samples have been heat-treated at four different temperatures to ob-tain a range of grain sizes. The procedures are listed in table 4.4, images of the mi-crostructures can be found in appendix D.

Table 4.4: Heat-treatments and recrystallisation of Al 51st

Set Heat-Treatment Grain size (std) [ �� ] Set Heat-Treatment Grain size (std) [ �� ]2 1h 248 �� 1 (0.3) 4 2h 480 �� 49 (18)3 1h 340 �� 87 (35) 5 2h 580 �� 60 (16)

Analysis of the microstructures shows a cross-sectional grain size distribution for therecrystallised samples, which is shown in figure 4.5. Relative small grains are situatedin the center of the cross-section, whereas an increase in size is observed towards theouter edge. This makes it difficult to do an accurate grain size measurement, becausethe position of the measurements becomes rather significant. Therefore the results forthe recrystallised sets (3 ,4 and 5 in table 4.4) should be considered as an indication ofthe mean grain size.Remarkably the average grain size of set 3 is larger than those for set 4 and 5. A rea-son for this phenomenon is hard to imagine, normally the grain size increases whenthe material is recrystallised at higher temperature. An increase of the recrystallisa-tion temperature decreases the amount of nuclei that are triggered, the process has lessstarting points. The growth rate however increases with increasing temperature andtherefore a higher temperature will lead to a larger grain size.


Figure 4.5: Grain size distribution of set 5

What not has been mentioned is that the samples have rested at room temperature formore than two weeks, after the recovery and recrystallisation heat-treatments. This hasbeen done because the material behaviour shows natural ageing, which has been dis-covered establishing a recrystallisation procedure. Hardness measurements showed aclear difference just after the heat-treatment and after one day.

0 250 500 750 1000 1250 150030

40

50

60

70

80

90

time [hours]

HV

Figure 4.6: Hardness in time (red = 1h 260 ��

, blue = 2h 505 ��

, black = 2h 634 ��

)

Therefore the hardness of three heat-treated samples have been measured over a pe-riod of about 2 months. The results are presented in figure 4.6, the values at zero arebefore and just after the heat-treatment. The sample heat-treated for 1 hour at 260 � �

shows no change in hardness, the temperature is too low to do a solid solution treat-ment.


For the two other specimens (blue and black) there is an increase in hardness for abouttwo weeks and then it stays on the same level. As can be seen the hardness increase ishigher for the sample heat-treated for two hours at 505 � �

.

This stronger increase can possibly be explained looking at diffusion. The alloying el-ements will diffuse through the grains towards the grain boundaries. The grain size ofthe sample heat-treated at 505 � �

is smaller than the grain size of the specimen heat-treated at 634 � �

. Therefore the diffusion occurs faster, the particles have to cover asmaller distance, resulting in a higher increase of the hardness.

In the following section the result of the mechanical testing of these compressed sam-ples will be shown.


4.2 Mechanical behaviour of MAC samples

As mentioned in the previous section the material behaviour of the samples, processedby multi axial compression, is measured performing compression and hardness exper-iments. These two tests have been chosen because of the shape of the specimens afterdeformation.

Figure 4.7: Different stages of sample preparation: before compression, after compression, machining and finallythe test specimen

As can be seen in figure 4.7 the deformed area is severely damaged at the surface.This cracked area has to be removed to get a good test sample. Therefore experimentswere chosen which could be done on relatively small samples, compression testing andhardness measurements are such methods. It is possible to obtain 2 or 3 samples, witha diameter and a height of 3 �� , from each deformed sample. The compression testinghas been done on a MTS 831.10 Elastomer test system equipped with a 15 kN loadcell,the samples are lubricated with molybdenum disulfide. In the following subsectionsthe test results for the two Al alloys will be presented.

4.2.1 LN1

Unfortunately only one sample of each set, with a height reduction of 50 � in thefirst hit, could be tested due to a lack of material. However, the compression testsfor the other Al alloy shows reproducible measurement results (3 tests per set), so thetechnique itself can be considered as representative for the material.

Table 4.5: Flow stress and true stress at a true strain of 0.5 (std)

Set Flow stress [MPa] True stress [MPa] Set Flow stress [MPa] True stress [MPa]A1 165 (-) 245 (-) B1 156.3 (23.8) 230.7 (9.5)A2 120 (-) 216 (-) B2 126.4 (12.1) 210.3 (1.8)A3 - - B3 37.9 (11) 217.9 (1.4)

The results of the compression tests for the LN1 alloy are shown in figure 4.8 andtable 4.5. The true stress is calculated under the assumption of volume invariance and


�� is used to calculate the true strain. As expected the flow stress decreases withincreasing grain size, there are less boundaries obstructing dislocation movement.

0 0.1 0.2 0.3 0.4 0.50

50

100

150

200

250

true strain [−]

true

str

ess

[MP

a]

A

as−deformed1h 248C

d = 0.96 µm

d = 1.8 µm

0 0.1 0.2 0.3 0.4 0.50

50

100

150

200

250

true strain [−]

true

str

ess

[Mpa

]

B

as deformed1h 248C2h 480C

d = 1.14 µm

d = 29 µm

d = 1.9 µm

Figure 4.8: (a) Results for samples with 50 � reduction in the first hit (b) Results for samples with 40 �reduction in the first hit

Looking at the total stress-strain curves for both sets A and B, the as-deformed mate-rial shows almost no strain hardening. And the two sets heat-treated at 248 � �

showonly little strain hardening. The reason for this is that with increasing heat-treatmentthe strain hardening is restored. Hardening is caused by the pile-up of dislocationsat barriers in the material. These barriers occur through dislocations, grain boundariesand second phase particles. For the as-deformed material and partly the recovered setsa huge amount of dislocations and grain boundaries are present. Migration of disloca-tions through the material cannot occur anymore, they are pinned at the barriers. Thestrain hardening mechanism is saturated for the as-deformed and recovered samples.Reducing the amount of grain boundaries and dislocations, makes it possible for theremaining or newly formed dislocations to migrate through the material. And thuspile-up re-occurs and the material behaviour shows a strain hardening effect.

The as-deformed material shows a relative high flow stress coupled with a high duc-tility, taken into account that the results are measured in compression. At a true strainof 0.5 the compressed sample is still intact. Normally if a high flow stress is obtainedthe ductility of the material will be poor and vice versa.

This kind of material behaviour has not been observed before for Al alloys in compres-sion testing. Valiev et al. [7] [8] investigated the mechanical behaviour of severely de-formed Cu an Ti samples, in tension and compression. It is shown that the as-deformedTi samples show also no strain hardening and a combination of high flow stress andductility in compression, however the ductility measured in tension is still low. Ten-sile results of the Cu samples on the other hand show both high flow stress and highductility. Clearly, it remains necessary to obtain tensile data for our experiments beforeconclusions can be drawn on the measured material behaviour.


0 5 10 15 20 25 3030

35

40

45

50

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60

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80

grain size [µm]

HV

A

0 5 10 15 20 25 3030

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40

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grain size [µm]

HV

B

Figure 4.9: (a) Hardness measurements for samples with 50 � reduction in the first hit (b) Hardnessmeasurements for samples with 40 � reduction in the first hit

The Vickers hardness measurements (figure 4.9) show a decrease in hardness withincreasing grain size, which is in accordance with the decrease in flow stress for thecompression experiments.

4.2.2 Al 51st

In figure 4.10 and table 4.6 the results from the compression and hardness measure-ments are shown.

0 0.1 0.2 0.3 0.4 0.50

50

100

150

200

250

300

350

true strain [−]

true

str

ess

[MP

a]

as−deformed1h 248C1h 340C2h 480C2h 580C

d = 0.9 µm

d = 1 µm

d = 87 µm

d = 49 µm

d = 60 µm

0 20 40 60 80 10030

40

50

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90

grain size [µm]

HV

Figure 4.10: (a) Compression results of Al 51st (b) Hardness measurements

The flow stress decreases with increasing grain size, but increases for sets 4 and 5.This behaviour can be explained taking the grain sizes into account. As mentioned inthe previous section the grain size of set 3 is somehow the largest, therefore the flowstress will have the lowest value. There are less barriers which hinder the dislocationmovement, because an increasing grain size decreases the total grain boundary area.The differences in the material behaviour, as observed for LN1, are also shown for thisAl 51st alloy. The coarse grained material, made by recrystallisation, shows the typicalmaterial behaviour, a relative low flow stress with significant strain hardening. As for


Table 4.6: Flow stress and true stress at a true strain of 0.5 (std)

Set Flow stress [MPa] True stress [MPa] Set Flow stress [MPa] True stress [MPa]1 218.2 (14) 262 (8.3) 4 109.7 (38.2) 282.1 (10.1)2 184.9 (7.9) 213.3 (2) 5 109.3 (13.5) 341.5 (15.4)3 57.8 (13.6) 176.4 (3.1)

the LN1 alloy the strain hardening effect is lost for the as-deformed material and thesamples heat-treated at 248 � �

. For these two sets a high flow stress and ductility canagain be observed.

In figure 4.10.b the Vickers hardness measurements are shown. As expected the hard-ness decreases with increasing grain size, but for the sample set with a grain size of60 �� a higher hardness is measured. This higher hardness might be caused by thestronger strain hardening this sample has as is shown in compression (figure 4.10. Areason for this stronger strain hardening however is not known yet.

4.3 Conclusions

The results from the compression experiments on the as-deformed material show ahigh flow stress in combination with a high ductility. The total grain boundary area forthese samples having a submicron grain size is large, there are a lot of obstacles whichimpede the dislocation movement. And thus the flow stress of this material is high. Ifthis high ductility in compression is also present in tension still has to be investigated.An other effect that can be observed is that the strain hardening effect is lost for theas-deformed and recovered samples. As mentioned before the governing hardeningmechanism is saturated, there are a huge number of obstacles in the material, throughwhich dislocations are pinned.The recrystallised samples exhibit the typical material behaviour, a relative low flowstress with significant strain hardening.

The Vickers hardness measurements show a decrease in hardness with increasing grainsize, for one exception as explained above. These results are in accordance with theresults obtained for the compression experiments.

Chapter 5

Conclusions

The goal of this project was firstly to investigate grain size-effects in micro-forming andsecondly to investigate grain size-effects for samples that have been made by MAC.Before discussing the results for punching and drawing, a statement can be made withrespective to the general macroscopic behaviour as mentioned in chapter 2. For clarityfigure 2.4 is shown again.

Figure 5.1: (a) Sketch of the commonly accepted relation between the flow stress and the ductility formacroscopic samples (b) Deviations found in this project (general and specific for this project(red))

The tensile results for the thin Al sheets deviate from the general macroscopic be-haviour, figure 5.1.b. A decrease in the flow stress is firstly combined with an increasein ductility, however beyond a certain level the ductility also decreases. As stated inchapter 3 this decrease in ductility can be observed when

� �is about 3. This decrease

in ductility can be attributed to the increasing importance the weakest grain and theorientation has on the material behaviour. At increasing grain size the mechanicalproperties of the weakest grain is not averaged anymore by adjacent grains. Thereforethe applied deformation will concentrate on this weak part and fracture will occur atlower strain levels.When the flow stress is plotted against � � � � , the materials seem to behave accordingto the Hall-Petch relation. The flow decreases with increasing grain size, there are lessconstraints against deformation, the dislocations can migrate more easily.

Chapter 5 Conclusions 35

For the MAC samples also a deviation from the general material behaviour can be ob-served, figure 5.1.b, the as-deformed and recovered samples show an indication of ahigh flow stress combined with a high ductility. Because these samples have a submi-cron grain size the amount of grain boundary area is large, there are a huge number ofobstacles which impede the movement of dislocations resulting in a high flow stress.Whether this high ductility can also be measured in tension, still has to be investi-gated.An other effect observed in compression is the loss of strain hardening. For the as-deformed and recovered samples the capacity for the accumulation of dislocations andhence strain hardening is limited.

Size-effects have also been investigated in punching and drawing experiments. Incontradiction to tensile and compression experiments, these two experiments are non-homogeneous, there are kinematic constraints for the deformation.The maximum shear strength and punching force for drawing both decrease uponincreasing grain size, but the decrease diminishes as the grain size becomes larger. Thedecrease can be attributed to the decrease in constraints against dislocation movement,the total grain boundary area decreases with increasing grain size.The deviation between the measurements becomes stronger with increased grain size,the number of grains in the deformation zones decreases. As a result the ’average’orientation of the grains in the deformation zones will vary stronger per sample withincreasing grain size and the deviation becomes stronger.For the tensile experiments a decrease in ductility has been observed if the grain sizeincreases, for the punching similar results are found. The punch displacement at themaximum shear strength increases first but then decreases as well. Again this can beattributed to the increased relative importance of the properties of the weakest grain.

Chapter 6

Recommendations

Foils� Decreasing the number of grains in the width of the samples, to cancel out aver-

aging in this direction as well. The grain size has to be increased, experiments onsingle crystals can be usefull in this context.

� For the punching and drawing experiments samples should be tested having abetter grain size range. Now especially for punching there is a large gap in sizebetween 79 �� and 442 �� .

� An other method to investigate size-effects is performing experiments on sampleswith a varying geometry and constant grain size. These experiments can givemore information on the surface effect.

� Measure EBSP with an orientation imaging microscope.

MAC� Further microstructural examination is necessary to obtain a better understanding

of the mechanical behaviour of the deformed material (EBSP measurements).� To obtain the necessary tensile data, a sample preparation method to obtain ten-

sile specimens from the deformed samples has to be found.

Bibliography

[1] Phillips, Rob, Crystals, Defects and Microstructures, Cambridge University Press,2001

[2] Kals, R.T.A., Fundamentals on the Miniaturization of Sheet Metal Working Processes,Meisenbach Verlag Bamberg 1999

[3] Kals, T.A., Eckstein, Ralf, Miniaturization in sheet metal working, Journal of Materi-als Processing Technology, 103 ,p.95-101 (2000)

[4] Nakamachi, E., Hiraiwa, K., Morimoto, H., Harimoto, M., Elastic/crystalline vis-coplastic finite element analysis of single- and poly-crystal sheet deformations and theirexperimental verification, International Journal of Plasticity, 16 , p. 1419-1441 (2000)

[5] Raulea, L.V., Goijaerts, A.M., Govaert, L.E., Baaijens, F.P.T., Size effects in the pro-cessing of thin metal sheets, Journal of Materials Processing Technology, 115 , p.44-48 (2001)

[6] Gholinia, Ali, Zwaag van der, S., Ultra-fine grain alloys project, The NetherlandsInstitute for Metals Research (NIMR/TUDELFT) (March 2002)

[7] Valiev, R.Z., Alexandrov, I.V., Zhu, Y.T., Lowe, T.C., Paradox of strength and ductilityin metals processed by severe plastic deformation, Journal of Materials Research, 17 ,No.1 (2002)

[8] Valiev, Zhu, Y.T., Jia, Y.M., Deformation behaviour and plastic instabilities of ultrafine-grained titanium, Applied physics letters, 79 , No. 5 (2001)

Appendix A

Sample preparation

In the table below the rolling data is presented.

Table A.1: Rolling procedureStrip thickness [mm] (total number of passes)

S1 0.55 (1) — 0.35 (3) — 0.30 (5) — 0.23 (6)S2 0.55 (1)— 0.40 (2) — 0.30 (3) — 0.21 (5)S3 0.77 (2) — 0.50 (6)— 0.30 (10)— 0.23 (11)S5 0.65 (1) — 0.46 (2) — 0.34 (4)S6 0.54 (1)— 0.33 (2) —0.32(3) — 0.26 (4)

Here some images of the microstructures after recrystallisation of the pure Al samples areshown.

Figure A.1: (a) Mean grain size of 3.1 �� (S5) (b) Mean grain size of 85 �� (S1)

Appendix A Sample preparation 39

Figure A.2: (a) Mean grain size of 107 �� (S2) (b) Mean grain size of 302 �� (S2)


Figure A.4: (a) Dual grain size of 4.6 and 225 �� (S6) (b) Mean grain size of 160 �� (S6)


Appendix B

Experimental data

Here the flow stress and strain at fracture are listed for the Al foil.

Table B.1: Flow stress and strain at fracture for the Al foil (std=standard deviation)Set Grain size[ �� ] Flow stress (std) [ �� ] Strain at fracture

1 (as-received) 1.9 148 (2.7) 0.032 1.8 137.9 (2.7) 0.033 3.3 105.4 (4.7) 0.074 38 25.9 (2) 0.275 71 27.8 (2) 0.17

Appendix C

Microstructures of MAC samples

Here images of the heat-treated Al 51st samples are shown.

Figure C.1: (a) Microstructure of set 2 (Al 51st) (b) Microstructure of set 3 (Al 51st)

Figure C.2: (a) Microstructure of set 4 (Al 51st) (b)Microstructure of set 5 (Al 51st)

To be able to compare the distribution of the intermetallics images have been taken at the samescale for all recrystallised samples. These images are presented below.

Appendix C Microstructures of MAC samples 42

Figure C.3: Microstructure of set 2 (Al 51st)




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