Abstract Predicting springback in the bending of magnesium sheet is difficult because it has high mechanical anisotropy leading to significant differences in the material behaviour in tension and compression. The tension/compression yield mismatch in magnesium is affected by the twinning behaviour which depends on the grain size and the direction of loading in regard to the crystal (C-axis) orientation. In this study the C-axis orientation of magnesium sheet was controlled by cutting sheets from a hot rolled block. Combined with heat treatment to produce different conditions for grain size and material strength this enabled for the first time to separately analyse the effect of material strength, grain size and C-axis orientation on the springback of AZ31 sheet metal. Pure and V-bending tests were performed and combined with advanced Digital Image Correlation (DIC) to experimentally determine the neutral layer shift for different levels of outer fibre bending strain before and after springback. Our study shows that springback in AZ31 reduces with increasing grain size but that it does not change with the C-axis orientation despite a reversal in the neutral layer position. The variation of springback shows more correlation with the bending yield strength measured directly from the pure bend test rather than the tensile yield strength and strongly correlates with the change in neutral layer shift in relation to grain size. Based on the experimental results analytical equations were developed to account for the effect of grain size on springback in magnesium. The model assumes the fully plastic, plane strain bending of strip and takes into account the effect of the tension/compression yield mismatch on the neutral layer position to determine the resulting bending moment. The developed equations provide, for the first time, a simple and clear mathematical explanation for the effect of material anisotropy (Yield strength mismatch) on the bending behaviour and springback of magnesium. If tuned with experiments, the model enables the estimation of springback as a function of the microstructure (grain size) in industrial practice.

中文翻译：

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显微组织对弯曲主导成形镁板材料行为的影响

摘要 镁板弯曲时的回弹难以预测，因为它具有很高的机械各向异性，导致材料在拉伸和压缩方面的行为存在显着差异。镁的拉伸/压缩屈服不匹配受孪晶行为的影响，孪晶行为取决于晶粒尺寸和关于晶体（C 轴）取向的加载方向。在这项研究中，镁板的 C 轴取向是通过从热轧块上切割板来控制的。结合热处理产生不同的晶粒尺寸和材料强度条件，这使得第一次能够单独分析材料强度、晶粒尺寸和C轴取向对AZ31金属板回弹的影响。执行纯和 V 型弯曲测试，并结合先进的数字图像相关 (DIC) 来实验确定回弹前后不同水平的外纤维弯曲应变的中性层位移。我们的研究表明，AZ31 中的回弹随着晶粒尺寸的增加而降低，但尽管中性层位置发生反转，但它不会随 C 轴取向而改变。回弹的变化与直接从纯弯曲试验测量的弯曲屈服强度而非拉伸屈服强度显示出更多的相关性，并且与与晶粒尺寸相关的中性层位移的变化密切相关。基于实验结果，开发了分析方程来解释晶粒尺寸对镁回弹的影响。该模型假设完全塑性，带材的平面应变弯曲，并考虑拉伸/压缩屈服不匹配对中性层位置的影响，以确定产生的弯矩。开发的方程首次为材料各向异性（屈服强度不匹配）对镁的弯曲行为和回弹的影响提供了简单而清晰的数学解释。如果通过实验进行调整，该模型可以在工业实践中将回弹估计为微观结构（晶粒尺寸）的函数。材料各向异性（屈服强度不匹配）对镁的弯曲行为和回弹的影响的简单而清晰的数学解释。如果通过实验进行调整，该模型可以在工业实践中将回弹估计为微观结构（晶粒尺寸）的函数。材料各向异性（屈服强度不匹配）对镁的弯曲行为和回弹的影响的简单而清晰的数学解释。如果通过实验进行调整，该模型可以在工业实践中将回弹估计为微观结构（晶粒尺寸）的函数。