Quenching and partitioning (Q&P) steels, as one of the third-generation advanced high strength steels, exhibit complex anisotropic hardening behavior under biaxial non-proportional loadings. In this study, a wide range of strain path changes (SPCs) defined as an angle ($\chi$) between stress deviators before and after the SPC is experimentally applied to characterize the anisotropic hardening of a Q&P steel with a strength grade of 980 MPa (QP980). The investigated SPCs include uniaxial tension followed by compression (UT-UC; $\chi$=180°), uniaxial compression followed by tension (UC-UT; $\chi$=180°), uniaxial tension followed by plane strain (UT-PS; $\chi$=30°), equi-biaxial tension followed by plane strain (EBT-PS; $\chi$=30°), followed by uniaxial tension (EBT-UT; $\chi$=60°) and followed by simple shear (EBT-SH; $\chi$=90°). These SPCs are achieved by the program-controlled biaxial tensile testing equipment using novel arm-reinforced cruciforms. The experimental findings in the QP980 steel sheet are summarized as follows: (1) Strong strain-dependent Bauschinger effect, transient hardening and permanent softening are observed in both UT-UC and UC-UT loadings; (2) Bauschinger effect increases as strain increases, and it exhibits obvious tension-compression asymmetry; (3) The transient hardening behaviors are path-dependent under SPCs with various $\chi$; (4) The Bauschinger coefficient is approximately a parabola function of $\text{cos}\chi$; (5) The most significant strength softening occurs under EBT-SH loading. In order to describe the complex hardening behavior of the QP980 steel, a distortional hardening model is proposed on the basis of non-associated flow rule. A coupled quadratic and stress-invariant-based yield function is used to describe stress anisotropy, strength differential effect, and anisotropic hardening for proportional loadings. Then, the Bauschinger effect related hardening and path-dependent permanent softening are captured by a modified homogeneous anisotropic hardening model. The calibrated model parameters and experimental validations demonstrate that the strain- and path-dependent Bauschinger effect can be well predicted by the proposed constitutive model. Especially, the model enables to accurately describe both the asymmetric anisotropic hardening and yield surface distortions of the QP980 steel at various biaxial SPCs.

淬火配分（Q&P）钢作为第三代先进高强钢之一，在双轴非比例载荷下表现出复杂的各向异性硬化行为。在这项研究中，广泛的应变路径变化 (SPC) 定义为角度 ($\chi$) 在实验应用 SPC 之前和之后的应力偏差之间，以表征强度等级为 980 MPa (QP980) 的 Q&P 钢的各向异性硬化。研究的 SPC 包括单轴拉伸和压缩 (UT-UC;$\chi$=180°），单轴压缩后拉伸（UC-UT；$\chi$=180°），单轴拉伸，然后是平面应变（UT-PS；$\chi$= 30°），等双轴拉伸，然后是平面应变（EBT-PS；$\chi$=30°），然后是单轴拉伸（EBT-UT；$\chi$=60°），然后是简单剪切（EBT-SH；$\chi$=90°）。这些 SPC 是通过程序控制的双轴拉伸测试设备使用新型臂加固十字形实现的。QP980 钢板的实验结果总结如下： (1) 在 UT-UC 和 UC-UT 载荷中观察到强应变相关的包辛格效应、瞬时硬化和永久软化；(2) 包辛格效应随着应变的增大而增大，呈现明显的拉压不对称性；(3) 瞬态硬化行为在 SPC 下具有路径相关性$\chi$; (4) 包辛格系数近似为抛物线函数$\text{因}\chi$; (5) 最显着的强度软化发生在 EBT-SH 加载下。为了描述QP980钢的复杂硬化行为，提出了一种基于非关联流动规律的变形硬化模型。耦合二次和基于应力不变的屈服函数用于描述应力各向异性、强度微分效应和比例载荷的各向异性硬化。然后，通过改进的均匀各向异性硬化模型捕获与包辛格效应相关的硬化和路径相关的永久软化。校准的模型参数和实验验证表明，所提出的本构模型可以很好地预测应变和路径相关的包辛格效应。尤其，