Vol. 1. STRAIN HARDENING AND SOFTENING OF METALS PRODUCED BY CYCLES OF PLASTIC DEFORMATION by P. W. J. OLDROYD B.Sc.(Eng.), A.C.G.I., D.I.C., A.M.I.Mech.E.. Thesis submitted for the degree of Doctor of Philosophy in the Facelty of Engineering of the: University of London Mechanical Engineering Department January 1968 City and Guilds College Imperial College of Science and Technology ... 7)- Cyclic tansion-compression tests between fixed limits of plastic strain, some tests between fixed limits of stress and certain other tests were made on the- following materials: 014'i-IC co per and aluminium in the annealed and cold-worked states.; En25 steel in the annealed and hardened and tempered states; and fully soft austenitic stainless steel. Copper arid aluminium subjected to cyclic plastic deformation between strain limits harden or soften according to their initial state: and the strain ampl- itude.; they behave in a similar manner when stress limits are used. There appears to be a settled cyclic state for each strain (or stress ) amplitude. In stress cycling a progressive change of the mean strain (cyclic creep) is observed. This is very sensitive to changes in the mean stress and it is sug- gested that it will always develop, whatever the value of the mean stress, because of geometrical instability. Annealed or tempered En25 steel has a yield step in its stress-strain curve for the -first loading but if the yield stress is exceeded. the step is not pres- ent in the curves for immediate re-loading in the same, or opposite, direct- ion. If the strain is not sufficiently great for this then cyclic deformat- ion causes a gradual removal of the conditions responsible for the stop and and this change reveals itself in a softening of the material. If the ampl- itude of plastic strain is small considerabl softening can occur. The ann- ealed steel does not significantly soften when cycled at strain amplitudes which are sufficiently large to eliminate the yield step at the first loading. The hardened steel softens significantly at all strain amplitudes near to or above the yield step strain. Soft austenitic stainless steel at first behaves in a similar manner to copper and aluminium but after a number of cycles - a number which depends on the strain amplitude - a sudden transition to rapid hardening occurs. The elimination of • asymmetry between the tension and compression proper- ties (the Bauschinger effect) by the use of decreasing cycles of plastic def- ormation suggests that hardness - as measured by these. properties - has both intrinsic and extrinsic components. Simple analogue models for cyclic behav- iour show only phenomena as:ic,ciated with the latter effect. A Method of predicting the cyclic behaviour of some metals from tne res- ults obtained from simple reversed loading tests is proposed. -3- ACKNOWLEDGMENTS' The author has pleasure in recording his indebtedness to Dr. P. P. Benham and Dr. D. J. Burns: to the former for having_introduced him to this field of research and encouraged him to undertake the present work; and to the latter for his guidance in the development of the investigation and - in particular - for his eneonragement in thetaek'of interpreting anddeser ibing the results of thereseereh. The laboratory and workshop staff of the Department of Mechanical Engineering are thanked fdr help in the development of the apparatus and for their care in the manufacture of the specimens, as well as for their co-operation in the day to day conduct of the testa. The staff of Instron_Ltd. are thanked for their advice and assistance during the development of the test equipment. The work was finances ,;by.. -thiy:.,(then)...,Department of Scientifib; and Industrial Research. The copper was processed by Imperial Metal Industr- ies (Kynoch):.Ltd.!..and Ahe:711.11Mitium donated and processed Industries Ltd.. The two firms are also thanked for their advice on the, problems met in the cold-working of the materials. LIST OF CONTENTS Page INTRODUCTION 8 2 LITERATURE REVIEW UP TO 1961 20_ 2.1 Extent of Review. 20 2.2 Early development of interest. 20 2.3 Renewal of Interest of Recent Years. 25 2.5.1 Effects of cycling on the stress-strain curve to fracture. 25 2.3.2 The effect of cycling on the indentation hardness. 27 2.3.3 The stress-strain curve during strain cycling. 28 2.3.4 The stress-strain curve during stress cycling. 33 2.!3.5 Energy changes during cyclic plastic deformation. 38 ,..6 The Bauschinger effect. 40 3 DESCRIPTION OF THE APPARATUS AND SPECIMENS 45 3.1 ;general. 4.5 The Testing Machine. 45 Drive system. 45 r.2 Load weighing system 45 .:2.3 Strain measuring system. 46 ..5 The Specimen and End-Fittings. 48 .3.'5.1 Choice of shape. 48 .!,.2 The. end-fitting. 50. 3.3.3 Variation of stress across the test section. 51 The Diametral Extensometer and Modified Chart Drive $y stem. 54. Page 3.4.1 General. 54 3.4.2 The extensometer. 55 3.4.3 The modified circuit. • 57 3.5- Calibration of the Scales. 58 3.5.1 Calibration of the stress scale. 58 3.5.2 Calibration of the strain scale. 60 3.6 The Strain Cycling Controls. 63 3.6.1 General. 63 3.6.2 Modifications to the crosshead cycling control system. 64 3.6.3 Plastic strain limit control. 65 4 MATERIALS AND RESULTS 67 4.1 Copper. 67 4.1.1 Condition as Supplied. 67 4.1.2 Annealed specimens. 4.1.3 Stretched specimens. 67 .4.1.4 Swaged specimens. 68 4.1.5 Cold drawn specimens. 69 4.1.6 Roller swaged specimens. 69 4.2 Aluminium. 70 4.2.1 Condition as supplied. 70 4.2.2 Annealed specimens. 71 4.2.3 Cold drawn specimens. 71 4.3 En25 Steel. 72 4.3.1 Condition as supplied. 72 -6- Page 4.3.2 Annealed specimens. 72 4.3.3 Hardened and tempered specimens. 72 4.4 Stainless Steel. 72 4.4.1 Condition as supplied 72 4.4.2 Specimens. 73 4.5 Results for Tests on Copper. 73 4.5.1 Cyclic tests between fixed limits of plastic strain. 73 4.5.2 Cyclic tests between fixed limits of nominal stress. 77 4.5.3 Other tests. 88 4.6 Results of Tests on Aluminium. 94 4.6.1 Cyclic tests between fixed limits of plastic strain. 94- 4.6.2 Cyclic tests between fixed limits of nominal stress. 94 4.6.3 Other tests. 96 4.7 Results for Tests on En25 Steel. 97 4.7.1 Cyclic tests between fixed limits of plastic strain. 97 4.7.2 Cyclic tests between fixed limits of nominal stress. 100 4.7.3 Other tests. 100 4.8 Results of Tests on Stainless Steel. .104 4.8.1 Cyclic tests between fixed limits of plastic strain. 104 4.8.2 Cyclic tests between fixed limits of nominal stress. 106 4.8.3 Other tests. 107 5 DISCUSSION 108 5.1 Survey of Cyclic Tests Between Fixed Limits of Plastic Strain. 108 5.1.1 Effect of various initial states on the cyclic behavioUr. 108 -7- 5.1.2 Effect of step changes on cyclic behaviour. 116 5.1.3 Cyclic behaviour of metallurgically unstable metal. 117 5.2 Survey of Cyclic Tests Between Fixed Limits of Stress. 119 5.2.1 Effect of equal stress limits in tension and compression. 119 5.2.2 Cycling between stress limits within the elastic range. 123 5.2.3 Effect of large values of mean stress. 127 5.3 The Bauschinger Effect and Cyclic Behaviour. 130 5.3.1 The presence of the Bauschinger effect in a symmetrical cycle.130 5.3.2 The removal of the Bauschinger effect by decreasing cycles. 134 5.3.3 The prediction of cyclic behaviour from Bauschinger tests. 138 ' 5.4. Analogue Models of Cyclic Behaviour. 143 5.4.1 General. L 143 5.4.2 Models consisting of pin-jointed bars. 143 5.4.3 Models consisting of springs and sliding blocks. 145 5.4.4 Spring-block models with changing chgracteristics. 148 .5.5 Cyclic Behaviour in the Light of Dislocation Theory. 14-9 6 CONCLUSIONS 151 Table 1. AnalyAis of. Aluminium. 156 Table 2 Analysis of Steels. 156 References. 158 Volume 2 contains the Figures. List of Figures. 163 1 INTRODUCTION . When a metal is subjected to cycles of plastic deformation between strain limits the stress range may change significantly during cycling, particularly in the first few cycles (1 ). The terms strain hardening and softening are used to describe such increases and decreases in stress range, since they are accompanied by corresponding changes in indentation hardness (2). A related effect is the progressive defor- mation (cyclic creep) which occurs: when ductile metalaare sUbjected to cycling between stress limits sufficient to cause plastic defor- mation (5). The behaviour of metals under cycles of plastic deformation is of interest to the engineer for two reasons:. Firstly, 'that he may understand the behaviour of structures in which some parts undergo cycles of plastic deformation; and secondly, that he may be able to use cyclic plastic deformation advantageously in the cold-working of metals. An understanding of the above phenomena is essential for the / development of reliable design procedure for the low endurance t<10 cycles) fatigue region. Structures which will undergo only a3 few cycles of deformation during their working life can be designed to operate with very high working stresses; which may sometimes exceed the elastic limit of the material.