Deformation-induced twinning is an important mechanism in metals with a limited number of slip deformation modes. The mechanisms for twin nucleation and growth are not completely understood, and modelling these processes is challenging because of the different length and time scales involved. Twins grow at the speed of sound up to a length of several millimetres and thickness of only a few microns. We present a phase field model for twinning, coupled with a dislocation-density based model for slip, implemented within the crystal plasticity finite element method. Softening of the critical resolved shear stress for twinning is used to reproduce the shear localisation that is typical of twin bands. Two interaction terms are introduced. The first one is a non-local term that models the interaction between residual dislocations at the twin interface and mobile dislocations in untwinned regions. The second is a local term that models the hardening of the twin system due to the presence of dislocations. By introducing these interaction terms, it is possible to reproduce a discrete pattern of twin bands after deformation. These interaction terms and interaction strength parameters determine the nucleation and spatial position of twins, twin thickness and number density of twins as a function of strain. The model is validated by comparing the simulated twin phase field with the dynamic formation of twins in tension, as measured by electron backscatter diffraction experiments on α-uranium. This model sheds light on the mechanism that determines twin growth and twin thickness. Specifically, twins stop thickening after a critical density of residual dislocations at the twin interface is reached. The interaction coefficients are interpreted in terms of the stacking fault energy in order to apply the model to different metals.

变形引起的孪生是在滑移变形模式数量有限的金属中的重要机制。孪晶成核和生长的机理尚未完全理解，并且由于涉及的时间长度和时间尺度不同，对这些过程进行建模具有挑战性。双胞胎以声音的速度生长，长度达到几毫米，厚度只有几微米。我们提出了一种在结晶可塑性有限元方法中实现的孪生相场模型，以及基于滑移的位错密度模型。用于孪生的临界解析剪切应力的软化用于复制典型的双带剪切局部化。介绍了两个交互术语。第一个是非本地术语，用于模拟双晶界面处的残余位错与未缠绕区域中的移动位错之间的相互作用。第二个是本地术语，用于模拟由于位错而导致的孪晶系统的硬化。通过引入这些相互作用项，可以在变形后再现双带的离散图案。这些相互作用项和相互作用强度参数决定了孪晶的形核和空间位置，孪晶的厚度和孪晶的密度作为应变的函数。通过将模拟的双相场与双胞胎在张力下的动态形成进行比较来验证该模型，这是通过电子背散射衍射实验测量的。第二个是本地术语，用于对由于位错而导致的孪晶系统硬化进行建模。通过引入这些相互作用项，可以在变形后再现双带的离散图案。这些相互作用项和相互作用强度参数决定了孪晶的形核和空间位置，孪晶的厚度和孪晶的数密度作为应变的函数。通过将模拟的双相场与双胞胎在张力下的动态形成进行比较来验证该模型，这是通过电子背散射衍射实验测量的。第二个是本地术语，用于对由于位错而导致的孪晶系统硬化进行建模。通过引入这些相互作用项，可以在变形后再现双带的离散图案。这些相互作用项和相互作用强度参数决定了孪晶的形核和空间位置，孪晶的厚度和孪晶的数密度作为应变的函数。通过将模拟的双相场与双胞胎在张力下的动态形成进行比较来验证该模型，这是通过电子反向散射衍射实验测量的。这些相互作用项和相互作用强度参数决定了孪晶的形核和空间位置，孪晶的厚度和孪晶的数密度作为应变的函数。通过将模拟的双相场与双胞胎在张力下的动态形成进行比较来验证该模型，这是通过电子背散射衍射实验测量的。这些相互作用项和相互作用强度参数决定了孪晶的形核和空间位置，孪晶的厚度和孪晶的数密度作为应变的函数。通过将模拟的双相场与双胞胎在张力下的动态形成进行比较来验证该模型，这是通过电子背散射衍射实验测量的。α-铀 该模型阐明了确定孪生生长和孪生厚度的机制。具体而言，在达到孪晶界面处的残余位错的临界密度之后，孪晶停止增厚。为了将模型应用于不同的金属，将根据堆垛层错能量来解释相互作用系数。