Resarch on Elasto-Plastic Material with Microstructures

微结构弹塑性材料的研究

• 批准号: 05650083
• 负责人: NAGAKI Shigeru
• 金额: $ 1.41万
• 依托单位: OKAYAMA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1993
• 资助国家: 日本
• 起止时间: 1993 至 1994
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-05650083/
• 关键词: Plasticity; Couple stress theory; Constitutive equation; Microstructure; Porous material; Anisotropic yield function; Perforated sheet

Directors and slip vectors were introduced to the theory of plastic materials with microsturcutes in the rage of the finite deformation. The relation between the proposed theory and the couple stress thory of elasticity together with the higher order strain gradient theory was discussed thoretically. The constitutive relation considering couple stress for plastic materials was also developed and an example of the rate-type constitutive equation was derived, where the yeild condition depends on not only the usual Cauchy stress but also the couple stress.To obtain the further mathematical form of constitutive equations for the real material with microstructures, we adopted the material with voids (i.e.porous material) as a model of materials with microstructures and the elastic-plastic behavior of perforated sheets were investigated experimentally.The yield stresses of perforated sheets with quasi-randomly distributed holes experimentally obtained can be simulated in the first approximation by the anisotropic yield function proposed by one of investigators. Evaluating the void distribution by the stereological method together with the use of Dirichlet tessellation, the effect of void spacing during plastic deformation can be treated quantitatively. This means that the procedure proposed here may become a useful tool for evaluating the overall plastic property of the material with microstructures, though a further examination will be necessary for precise description of the resulting anisotropic behavior of perforated sheets.

在有限变形范围内，将指向矢和滑移矢量引入细观塑性材料理论。从理论上讨论了该理论与弹性力学偶应力理论和高阶应变梯度理论的关系。建立了考虑偶应力的塑性材料本构关系，并给出了率型本构方程的一个实例，其中屈服条件不仅取决于通常的Cauchy应力，而且还取决于偶应力.为了得到含微结构的真实的材料本构方程的进一步数学形式，我们采用了有空隙的材料对多孔材料作为微结构材料的模型和多孔板的弹塑性行为进行了实验研究，得到了准多孔板的屈服应力实验上获得的随机分布的孔可以通过由研究者之一提出的各向异性屈服函数在第一近似下模拟。用体视学方法和狄利克雷曲面拟合相结合的方法计算孔洞分布，可以定量地处理孔洞间距对塑性变形的影响。这意味着，这里提出的程序可能成为一个有用的工具，用于评估材料的整体塑性与微观结构，虽然进一步的检查将是必要的精确描述所产生的各向异性行为的穿孔板。