Alloy softening in Ni3Al polycrystals

The alloying effect of boron on localized deformation in Ni₃Al polycrystals containing 24–26 at% AI was studied using microhardness indentation. Alloy softening was observed both along the grain boundaries and in the grain interior. The softening effect decreased as the aluminium concentration increased. For alloys of near-stoichiometric composition, the maximum effect occurred at about 0.23 at% (500 wt p.p.m.) boron. A softening mechanism based on cross slip of screw dislocations was proposed.     

Stress-strain curves of superplastic alloys

Force-elongation and stress-strain curves have been analysed for superplastically deformed alloys tested in uniaxial tension under constant cross-head velocity conditions. By considering instability criteria the curves can be divided into three characteristic stages. In the course of the first two stages the samples are work hardened while during the third stage no work hardening takes place, although 85 to 90% of the total deformation occurs at this stage. However, sometimes at the end of stage III a weak strain hardening appears again due to grain growth. From the analysis of stage III the strain-rate sensitivity can be determined in good agreement with other methods.     

Solid-solution hardening and softening in binary iron alloys

Six dilute (0.2, 0.5 and 1 at %) binary iron-base alloys with Co, Cr, Al, Si, Mn and Ni were prepared after scavenging inherent carbon with Ti. From tensile and stress relaxation tests in the temperature range of 77 to 450 K, stress-strain behaviours and thermal activation parameters were analysed as functions of solute content and temperature. In the four alloys containing Ni, Mn, Al and Si, solid-solution softening occurs below 250 K while solid-solution hardening occurs above 250 K. In the alloys containing Co or Cr, neither softening nor hardening due to solute additions occurs at any temperature. Detailed analysis of thermal activation parameters leads one to conclude that the solid-solution softening in the above mentioned four alloys is due to a decrease in kink energy with increasing solute content, while in the latter two alloys no change in kink energy occurs. On the other hand, there exists a strong solute concentration dependence of the athermal component, suggesting that the solid-solution hardening is due to the interaction of dislocations with groups of substitutional solute atoms that create lattice and modulus misfits.     

Strain hardening and orientation hardening/softening in cold rolled AA 5052 aluminum alloy

The tensile properties of cold rolled sheets were measured for the hot band and annealed hot band of AA 5052 aluminum alloy. The variation in yield strength with rolling true strain was used to represent the hardening rate of cold rolled sheets. The Taylor factor (M?) of cold rolled sheets in tension along the rolling direction was calculated based on the measured orientation distribution functions. The strain hardening and orientation hardening/softening produced by cold deformation were analyzed. The results show that the contribution to the hardening rate of cold rolled sheets comes largely from the deformed microstructure and partly from the texture change. For the annealed hot band the orientation softening occurs at strains below 0.5, while the orientation hardening occurs at strains over 0.5. For the hot band the dM?/dε value is always positive, indicating that orientation softening does not occur.     

Work softening and work hardening during rotary swaging of copper

Abstract

Cold–worked and annealed copper rods were deformed at room temperature in a four–die rotary swaging machine. The outer parts of the cold–worked rods were work softened, whereas the annealed rods were inhomogeneously work-hardened, with a strength increase from the surface to the core. Both effects can be explained as being a consequence of a cyclic deformation during rotary swaging.

MST/148     

Studies on FRP-concrete interface with hardening and softening bond-slip law

This latest experimental study proposes a theory that the bond-slip law for a FRP-concrete interface contains linear hardening and exponential softening. On the basis of this law, the paper studies the mechanic behavior and debonding process of a FRP-concrete interface. Firstly, through nonlinear fracture mechanics, the analytical solutions of the interface shear stress, the axial normal stress of FRP and the load–displacement relationship at the loaded end with the single shear test model of FRP-concrete are acquired. The shear stress propagation as well as the debonding process of the whole interface for different bond lengths could be predicted. Secondly, a simplified interface bond-slip law is used by changing the exponential softening law into a linear softening law. In addition, the analytical solutions for the simplified interface bond-slip law could also be obtained. Finally, based on the analytical solutions of the two bond-slip laws, the influences of the FRP bond length and stiffness on load–displacement curve and the ultimate load, as well as stiffness on effective bond length were discussed, with the similarities and differences between the two bond-slip laws also being studied.     

An extended crystal plasticity model for latent hardening in polycrystals

In this contribution, a computational approach to modeling size-dependent self- and latent hardening in polycrystals is presented. Latent hardening is the hardening of inactive slip systems due to active slip systems. We focus attention on the investigation of glide system interaction, latent hardening and excess dislocation development. In particular, latent hardening results in a transition to patchy slip as a first indication and expression of the development of dislocation microstructures. To this end, following Nye (Acta Metall 1:153–162, 1953), Kondo (in Proceedings of the second Japan national congress for applied mechanics. Science Council of Japan, Tokyo, pp. 41–47, 1953), and many others, local deformation incompatibility in the material is adopted as a measure of the density of geometrically necessary dislocations. Their development results in additional energy being stored in the material, leading to additional kinematic-like hardening effects. A large-deformation model for latent hardening is introduced. This approach is based on direct exploitation of the dissipation principle to derive all field relations and (sufficient) forms of the constitutive relations as based on the free energy density and dissipation potential. The numerical implementation is done via a dual-mixed finite element method. A numerical example for polycrystals is presented.     

Micromechanical modelling of strain hardening and tension softening in cementitious composites

This paper will describe a procedure for modelling the complete macroscopic response (including strain hardening and tension softening) of two short fibre reinforced cementitious composites and show how their microstructural parameters influence this response. From a mathematical point of view it is necessary to examine how bridging forces imposed by the fibres alter the opening of multiple cracks in elastic solids under unidirectional tensile loading. The strain hardening is essentially due to elastic bridging forces which are proportional to crack opening displacements. After a certain critical crack opening displacement is reached, some fibres progressively debond from the elastic matrix and thereafter provide a residual bridging force by frictional pull-out, while others continue to provide full bridging. This results in a kind of elasto-plastic bridging law which governs the initial tension softening response of the composite. Besides the usual square-root singularity at crack tips, the elasto-plastic bridging law introduces a logarithmic singularity at the point of discontinuity in the bridging force. These singularities have been analytically isolated, so that only regular functions are subjected to numerical integration. Unbridged multiple crack problems have in the past been solved using double infinite series which have been found to be divergent. In this paper a superposition procedure will be described that eliminates the use of double infinite series and thus the problem of divergence. It is applicable to both unbridged and bridged multiple cracks. The paper will end by showing how the model of multiple bridged cracks can accurately predict the prolonged nonlinear strain hardening and the initial tension softening response of two cementitious composites.     

Fatigue softening and hardening in mild steel detected from Barkhausen noise

The measurement of Barkhausen noise is used to follow the fatigue process in a mild steel. The variation in the root-mean-square (rms) value of the noise with bending stress during single-strain cycles and in unloaded samples is determined at several stages of fatigue life. The fatigue softening and hardening are found to be sensitively revealed by specific changes in the shape and area of the noise versus stress loops and also in the variation in the noise in unloaded samples, corresponding to changes in the residual stress state. The high sensitivity of the magnetic measurement technique is emphasized.     

Combined hardening and softening constitutive model of plasticity: precursor to shear slip line failure

 In this work, we present a finite element model capable of describing both the plastic deformation which accumulates during the hardening phase as the precursor to failure and the failure process leading to softening phenomena induced by shear slip lines. This is achieved by activating subsequently hardening and softening mechanisms with the localization condition which separates them. The chosen model problem of von Mises plasticity is addressed in detail, along with particular combination of mixed and enhanced finite element approximations which are selected to control the locking phenomena and guarantee mesh-invariant computation of plastic dissipation. Several numerical simulations are presented in order to illustrate the ability of the presented model to predict the final orientation of the shear slip lines for the case of non-proportional loading. Dedicated to the memory of Prof. Mike Crisfield, for his cheerfulness and cooperation as a colleague and friend over many years. This work was supported by the French Ministry of Research and ACI research program. This support is gratefully acknowledged.     

Effect of flow softening on ring test calibration curves

The application of the ring test to assess die–workpiece interface friction during forging of a flow softening material was investigated. Calibration curves were generated by conducting finite element method (FEM) simulations of ring forging with different friction factors. The method was validated by conducting isothermal, hot compression tests on rings of an α₂ titanium aluminide alloy for both lubricated and unlubricated interface conditions. The FEM results for the flow softening material were compared to those generated assuming no flow softening. In all cases, the differences between the curves predicted for the flow softening and non-softening behaviors were quite small. Furthermore, for given values of the interface friction factor, the calibration curves were essentially independent of the strain rate sensitivity (m) and flow softening.     

Uniaxial ratchetting in steels with different cyclic softening/hardening behaviours

The cyclic deformation of three structural steels, SS316L stainless steel, 40Cr3MoV bainitic steel and 25CDV4.11 steel, were studied experimentally by uniaxial cyclic straining or stressing tests at room temperature. The cyclic softening/hardening behaviours of the steels were discussed first by cyclic straining tests; and then the effects of cyclic softening/hardening behaviours on the uniaxial ratchetting of the materials were investigated by asymmetrical cyclic stressing tests. It is concluded from the experimental results that the ratchetting greatly depends on the cyclic softening/hardening behaviours of the materials, as well as the loading history. Different ratchetting and failure behaviours are observed for the prescribed steels. It is also stated that the proposed unified visco‐plastic constitutive model can provide a fairly reasonable simulation of the uniaxial ratchetting of SS316L stainless steel and 25CDV4.11 steel; but cannot simulate the ratchetting of 40Cr3MoV bainitic steel since the dependence of cyclic softening behaviours on the applied inelastic strain amplitude cannot be reasonably described in the discussed constitutive model. Some significant conclusions are obtained, which are useful to construct constitutive model to describe the ratchetting of the materials with different cyclic softening/hardening behaviours.     

Correlation of tensile and flexural responses of strain softening and strain hardening cement composites

Closed form equations for generating moment–curvature response of a rectangular beam of fiber reinforced concrete are presented. These equations can be used in conjunction with crack localization rules to predict flexural response of a beam under four point bending test. Parametric studies simulated the behavior of two classes of fiber reinforced concrete: strain softening and strain hardening materials. The simulation revealed that the direct use of uniaxial tension and compression responses under-predicted the flexural response for strain softening material while a good prediction for strain hardening material was obtained. The importance of strain softening range on the flexural response is discussed using non-dimensional post-peak parameters. Results imply that the brittleness and size effect are more pronounced in the flexural response of brittle materials, while more accurate predictions are obtained with ductile materials. It is also demonstrated that correlations of tensile and flexural results can be established using normalized uniaxial tension and compression models with a single scaling factor.