Bauschinger effect

In this chapter, we will review the effects of shock-wave deform.ation on material response after the completion of the shock cycle. The techniques and design parameters necessary to implement successful shock-recovery experiments in metallic and brittle solids will be discussed. The influence of shock parameters, including peak pressure and pulse duration, loading-rate effects, and the Bauschinger effect (in some shock-loaded materials) on postshock structure/property material behavior will be detailed. 

Shock-recovery experiments by Gray [10] were conducted to assess directly if the strain-path reversal inherent to the shock contains a traditional microstructurally controlled Bauschinger effect for a shock-loaded two-phase material. Two samples of a polycrystalline Al-4 wt.% Cu alloy were shock loaded to 5.0 GPa and soft recovered in the same shock assembly to assure identical shock-loading conditions. The samples had two microstructural... 

Figure 6.15. Stress-strain response of shock-loaded Al-4 wt.% Cu as a function of heat treatment illustrating the effect of the Bauschinger effect on the response of the 6 condition compared to the solution-treated microstructure.

Recent experiments by Gray et al. [47] have probed the contribution of the Bauschinger effect on real-time unloading wave profiles and postshock... 

Figure 6.16. Stress-strain of shock-loaded silicon bronze contrasted to the annealed alloy showing evidence of a Bauschinger effect.

Figure 6.17. VISAR wave profiles of copper and silicon bronze at 10 GPa exhibiting differing unloading wave shapes supporting a Bauschinger effect contribution to unloading.

G.T. Gray III, R.S. Hixson, and C.E. Morris, Bauschinger Effect During Shock Loading, in Shock Compression of Condensed Matter (edited by S.C. Schmidt, R.D. Dick, J.W. Forbes, and D.G. Tasker), Elsevier Science, New York, 1992, pp. 427-430. 

It is instructive to describe elastic-plastic responses in terms of idealized behaviors. Generally, elastic-deformation models describe the solid as either linearly or nonlinearly elastic. The plastic deformation material models describe rate-independent behaviors in terms of either ideal plasticity, strainhardening plasticity, strain-softening plasticity, or as stress-history dependent, e.g. the Bauschinger effect [64J01, 91S01]. Rate-dependent descriptions are more physically realistic and are the basis for viscoplastic models. The degree of flexibility afforded elastic-plastic model development has typically led to descriptions of materials response that contain more adjustable parameters than can be independently verified. 

M.F. Horstemeyer Damage influence on Bauschinger effect of a cast A 356 aluminum alloy. Scripta Mater. 39, 1491-1495 (1998)... 

H. Fang et al Atomistic simulations of Bauschinger effects of metals with high angle and low angle grain boundaries. Comp. Meth. App. Mech. Eng. 193, 1789-1802 (2004)... 

J.B. Jordon et al Damage and stress state influence on the Bauschinger effect in aluminum alloys. Mech. Matls 39, 920-931 (2007)... 

Armstrong PJ, Frederick CO (1966) A mathematical representation of the multiaxial Bauschinger effect. GEGB report RD/B/N731. Berkeley Nuclear Laboratories... 

Figure 8.1 shows stress-strain curves of atactic polystyrene (PS) in compression at 295 K for two structures with different initial states well annealed, i.e., furnace cooled from Tg + 20 K to room temperature, and rapidly quenched into ice water (Hasan and Boyce 1993). In both cases there is a gradual transition to fully developed plasticity that is reached at the peak of a yield phenomenon which is more prominent in the annealed material. Both curves show several unloading histories, starting with one close to the upper yield peak. All unloading paths show prominent Bauschinger effects of plastic strain recovery that is independent of the pre-strain. These indicate the presence of strain-induced back stresses and some recoverable stored elastic strain energy. In both cases the flow stress moves toward a unique flow state attained at a strain of around 0.3. 

Fig. 8.13 A true-stress-true-strain curve of PS, strained to an extensional true strain of 1.4 at T = 296 K, showing the emergence of a strain-hardening stage past the plateau of the flow state, at e = 0.4, with a number of stress removals showing Bauschinger effects (from Hasan and Boyce (1993) courtesy of Elsevier).

We illustrate the isotropic and kinematic hardening models for the onedimensional problem in Fig. 2.18a, b, and for the two dimensional problem in Fig. 2.19. Note that the behavior shown in Fig. 2.18b is known as the Bauschinger effect. In geotechnical engineering practice the isotropic hardening model is widely used because, except in earthquake situations, it is rare that the loading direction is completely reversed. 

Frequently, the term Bauschinger effect is used if the flow stress becomes smaller upon load reversal, like in kinematic hardening. 

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