Analysis of adiabatic shear coupled to ductile fracture and melting in viscoplastic metals

TL;DR

This work develops an analytical–numerical framework for adiabatic shear localization in viscoplastic metals that can undergo thermal softening, ductile fracture, and melting under simple shear with superposed pressure. It couples a power-law viscoplastic model to a ductile-damage and a solid–liquid phase-field melting description in a thermodynamically consistent way, and derives localization criteria alongside a method to compute the critical average shear strain $\bar{\gamma}_c$ and the accompanying stress decay. Applied to a Ni-Cr high-strength steel, the model reproduces dynamic torsion data up to localization and shows that, for realistic loading, damage and fracture preempt melting, with melting confined to narrow regions if fracture is suppressed; cohesive energy and external pressure modulate the localization behavior. Overall, the findings indicate that melting is not a primary driver of localization in this steel under studied conditions, while initial defects and tensile pressure significantly influence the onset and progression of shear bands, providing insight into damage evolution in high-strength steels under high-rate loading.

Abstract

Material failure by adiabatic shear is analyzed in viscoplastic metals that can demonstrate up to three distinct softening mechanisms: thermal softening, ductile fracture, and melting. An analytical framework is constructed for studying simple shear deformation with superposed static pressure. A continuum power-law viscoplastic formulation is coupled to a ductile damage model and a solid-liquid phase transition model in a thermodynamically consistent manner. Criteria for localization to a band of infinite shear strain are discussed. An analytical-numerical method for determining the critical average shear strain for localization and commensurate stress decay is devised. Averaged results for a high-strength steel agree reasonably well with experimental dynamic torsion data. Calculations probe possible effects of ductile fracture and melting on shear banding, and vice-versa, including influences of cohesive energy, equilibrium melting temperature, and initial defects. A threshold energy density for localization onset is positively correlated to critical strain and inversely correlated to initial defect severity. Tensile pressure accelerates damage softening and increases defect sensitivity, promoting shear failure. In the present steel, melting is precluded by ductile fracture for loading conditions and material properties within realistic protocols. If heat conduction, fracture, and damage softening are artificially suppressed, melting is confined to a narrow region in the core of the band.

Figures (8)

• Figure 1: Boundary value problem for simple shear with superposed static pressure: tangential velocity at $y=h$ is $\upsilon_0$, normal traction $t_n$ is $p_0$, including $t_n (z \rightarrow \pm \infty,t) = -p_0$. Slab is infinite in $X,x,Z,z$ directions; initial (current) height of slab is $h_0$ ($h$). Slab is thermally insulated: $\partial \theta / \partial y = 0$ at $y = 0$ and at $y = h$ for $t \geq 0^+$. Initial variable $\chi_0(y) = \chi(y,t = 0)$ and temperature $\theta(y,t=0)$ can vary modestly over $y \in (0,h)$.
• Figure 2: Model results and experimental torsion data fellows2001b: (a) average shear stress $\bar{\tau}$ vs. average shear strain $\bar{\gamma}$ (strain in rigid-plastic model shifted by $\gamma_o$ to compensate for oscillatory elastic ramp-up in experiments, not shown) (b) localized strain distribution $\gamma$, specimen size $h_0 = 2$ mm (c) two initial defect profiles ($\epsilon_0,\lambda_0$). Experimental points sample continuous (a) or discrete (b) data from Ref. fellows2001b.
• Figure 3: Model results for two initial defect profiles ($\epsilon_0,\lambda_0$) vs. normalized spatial position $\tilde{y}$: (a) post-localization strain $\gamma_c$ (b) temperature $\theta_c$ (c) fracture order parameter $\phi_c$
• Figure 4: Model results with features activated or suppressed: (a) average shear stress $\bar{\tau}$ vs. average shear strain $\bar{\gamma}$ and experimental torsion data fellows2001b; (b), (c), (d) homogeneous solutions for average shear stress, temperature $\bar{\theta}$, and melt order parameter $\bar{\xi}$ to extreme shear strain. Slow and fast melt correspond to respective large and small values of $\beta_\xi$ in Table \ref{['table1']}; $r_0^\xi$ is fraction of stored energy of cold work released upon melting.
• Figure 5: Model results without fracture for two initial defect profiles ($\epsilon_0,\lambda_0$) vs. normalized spatial position $\tilde{y}$: (a), (b) strain $\gamma_c$, temperature $\theta_c$ for $r^\xi_0 = 0$ or melt suppressed (c) melt parameter $\xi_c$ for $r^\xi_0 = 0,1$