Evaluation of non-linear sin²ψ distributions in residual stress analysis based on a scale-bridging mechanical modeling

该研究项目的目的是澄清在多晶、单相和多相金属材料状态的x射线（残余）应力分析中，在实验晶格应变与sin²ψ非线性依赖的情况下，如何可靠地确定残余应力（RS）的开放性问题。为了解决这一问题，通过加载实验将织构和塑性变形的影响分离开来。为了评估多轴向对微型rs发展的影响，进行了单轴和双轴加载实验（实验室和同步加速器实验）。本项目对铝合金（fcc）、铁素体钢（bcc）和双相钢（bcc/fcc）三种不同的材料体系进行了系统的研究。通过在弹性和弹塑性范围内的原位加载实验，对不同晶体结构的单相和两相材料在塑性变形过程中微rs的发展进行了全面的测量数据。为了能够进一步评价织构对微rs形成的影响，通过调整轧制程度来具体改变初始状态下材料的织构。对于RS分析的评估策略，通过双尺度模拟对微观RS进行建模，并通过傅里叶系数等降阶方法通过取向空间近似模拟塑性应变的分布。从连续介质力学的角度来看，目标是确定应力张量或弹性变形张量作为晶体取向函数的期望值。对于非织构和织构材料，以及单相和多相材料，都需要解决这个双尺度问题。考虑了两条路线。在第一种方法中，当施加宏观载荷时，塑性变形用平均场方法估计，或者用全场计算（FFT）来确定，其中包括晶体织构和塑性变形作为残余应变。由于计算时间大，目前还没有给出方法在路线1上的实际适用性。在第二种途径中，在途径1中获得的关于晶格应力统计特性的知识将使用平均场方法（奇异近似）和最大熵方法进行建模，而不解决单个晶体取向的塑性子过程。为此，必须在路线1中识别宏观塑性变形引起的自然应变的统计分布，并通过模型函数来描述。如果成功，一个计算RS的实用模型将作为最终结果。

The aim of the research project is to clarify the open question of how a reliable determination of the residual stresses (RS) can be carried out in the case of a non-linear dependence of the experimental lattice strains on sin²ψ in the X-ray (residual) stress analysis of polycrystalline, single-phase and multi-phase metallic material states. To solve this problem, the influences of texture and plastic deformation are experimentally separated from each other by loading experiments. The loading experiments (laboratory and synchrotron experiments) are carried out uniaxially as well as biaxially in order to evaluate the influence of multiaxiality on the development of micro-RS. Three different material systems, Al alloy (fcc), ferritic steel (bcc) and duplex steel (bcc/fcc), are systematically investigated in the project. With the help of in situ loading experiments in the elastic and elasto-plastic range, comprehensive measurement data on the development of the micro-RS during plastic deformation are determined for the single- and two-phase materials of different crystal structures. In order to be able to additionally evaluate the influence of the texture on the formation of the micro-RS, the textures of the materials in the initial state are specifically varied by adjusting the rolling degree. With regard to the evaluation strategy to be developed for the RS analysis, the micro-RS are modeled via two-scale simulations and the distribution of the plastic strains is approximated via the orientation space by order reduction approaches such as Fourier coefficients. From a continuum mechanics perspective, the goal is to determine the expected value of the stress tensor or elastic distortion tensor as a function of crystal orientation. This two-scale problem is to be solved for non-textured and textured as well as single and multi-phase materials. Two routes are considered. In the first route, the plastic deformations are estimated with mean-field methods when the macroscopic load is applied and alternatively determined with full-field calculations (FFT) by including the crystallographic texture and the plastic distortions as residual strains. Due to the large computing time, the practical suitability of the methods in route 1 is not yet given. In the second route, the knowledge gained in route 1 on the statistical properties of the lattice stresses is to be modeled using a mean-field approach (singular approximation) and the maximum entropy method, without resolving the plastic sub-processes for the individual crystal orientations. For this, the statistical distributions of the natural strains induced by macroscopic plastic deformations must be identified in Route 1 and described by model functions. If successful, a practical model for calculating RS would be available as the end result.