Localization, in the form of adiabatic shear, is analyzed in viscoplastic solids that may undergo structural transformation driven by pressure, shear stress, temperature, and magnetic field. As pertinent to polycrystalline metals, transformations may include solid–solid phase transitions, twinning, and dynamic recrystallization. A finite-strain constitutive framework for isotropic metals is used to solve a boundary value problem involving simple shearing with superposed hydrostatic pressure and constant external magnetic field. Three-dimensional theory is reduced to a formulation simple enough to facilitate analysis without advanced numerical methods, yet sophisticated enough to maintain the salient physics. Ranges of constitutive parameters (e.g., strain hardening, strain-rate sensitivity, thermal softening, and strain-driven structure transformation limits influenced by pressure and magnetic field) are obtained for which localization to infinite shear strain is possible. Motivated by experimental and theoretical studies suggesting a non-negligible role of shear on phase transformations in iron (Fe), the model is used to understand influences of pressure and phase transitions on applied strains for which localization should occur in pure Fe and a high-strength steel. Results show, among other trends for the two materials, that shear localization in conjunction with phase transformation is promoted when the transformed phase is softer than the parent phase. Localization that would occur in the isolated parent phase can be mitigated if strain hardening or thermal softening tendencies of the transformed phase are sufficiently increased or reduced, respectively.

中文翻译：

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具有压敏结构转变的粘塑性固体中的剪切定位分析


在粘塑性固体中分析绝热剪切形式的局部化，这些粘塑性固体可能在压力、剪切应力、温度和磁场的驱动下发生结构转变。与多晶金属相关，转变可能包括固-固相变、孪晶和动态再结晶。采用各向同性金属的有限应变本构框架求解具有叠加静水压力和恒定外部磁场的简单剪切的边界值问题。三维理论被简化为一个公式，它足够简单，无需高级数值方法即可进行分析，但又足够复杂，可以保持突出的物理特性。获得了本构参数的范围（例如，应变硬化、应变速率敏感性、热软化和受压力和磁场影响的应变驱动结构转变极限），可以定位到无限剪切应变。实验和理论研究表明剪切对铁 （Fe） 相变的作用不可忽视，该模型用于了解压力和相变对施加应变的影响，这些应变应在纯 Fe 和高强度钢中发生局域化。结果表明，除这两种材料的其他趋势外，当转化相比母相更软时，剪切局域化和相变会得到促进。如果转化相的应变硬化或热软化趋势分别得到充分增加或减少，则可以减轻在孤立的母相中发生的局域化。