Unified simulation of hardening and softening effects for metals up to failure

Toward accurately simulating both hardening and softening effects for metals up to failure, a new finite strain elastoplastic J2-flow model is proposed with the yield strength therein as a function of the plastic work in the explicit form. With no need to identify any adjustable parameters, the uniaxial stress-strain response predicted from this new model is shown to automatically and accurately match any given data from monotonic uniaxial extension tests of bars. As such, the objectives in three respects are achieved for the first time, i.e., (i) both the hardening and softening effects up to failure can be simulated in the sense of matching test data with no errors, (ii) the usual tedious implicit procedures toward identifying numerous unknown parameters need not be involved and can be totally bypassed, and (iii) the model applicability can be ensured in a broad sense for various metallic materials with markedly different transition effects from hardening to softening. With the new model, the complete response features of stretched bars and twisted tubes up to failure are studied, including the failure effects of bars under monotonic extension and tubes under monotonic torsion and, furthermore, the fatigue failure effects of bars under cyclic loading. The results show accurate agreement with the uniaxial data, and the results for both the shear stress and the normal stress at the finite torsion display realistic hardening-to-softening transition effects for the first time.