Influence of the bi-nonlinearity on the characterization of mode I fracture parameter [formula omitted] for a cracked giant magnetostrictive material in the coupled magneto-elastic field: An experimental and numerical study

Abstract

Terfenol-D, a giant magnetostrictive material exhibits bi-nonlinear stress-strain relationship in coupled magneto-elastic field. A novel hyperbolic vector generalized magneto-elastic constitutive model is employed to describe this bi-nonlinear stress-strain behaviour. Some physics-based experiments for magnetization and magnetostriction hysteresis loops and mechanical compression tests under the applied magnetic field are conducted. The general HM and stress-strain relationships are programmed in C language to define the coupled field constitutive material model. Coupled magneto-elastic response from the performed finite element analyses are compared with experiments to optimize the material parameters. Fracture experiments employing single edge notch bend (SENB) specimens are conducted with and without external magnetic field as per ASTM E399. The digital image correlation technique is used to capture the load line and crack opening displacement variation with peak fracture load data. Two parameter Weibull statistical theory of strength has been utilised to forecast the mean peak fracture load. The Weibull modulus and goodness of fit are assessed using linear regression analysis (LIN2), biased and unbiased maximum likelihood estimation (MLE2-B & MLE2-U) approach. Finite element crack propagation model based on the optimized nonlinear constitutive relations is built concerning to magnetization and stress dependent elasticity problem of Terfenol-D fracture. Three-dimensional J-integral is formulated considering the effects of magneto-elastic fields, which is subsequently used to characterize the crack front singularity near the fracture process zone. Critical strain energy release rate JIc was calculated using the mean peak fracture load in both absence and presence of the external magnetic field. Finally, the influence of bi-nonlinear modularity and applied external magnetic field on the fracture behaviour of the Terfenol-D SENB fracture specimen were compared with the unimodular experimental results and substantial differences were reported. The stipulation and importance of considering the bi-nonlinear critical strain energy release rate JIc in the context of a coupled magneto-elastic field was discussed certifying the observations.