A THEORY OF THE YIELDING AND PLASTIC FLOW OF ANISOTROPIC METALS
A THEORY OF THE YIELDING AND PLASTIC FLOW OF ANISOTROPIC METALS
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DOI：
10.1098/rspa.1948.0045
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发表时间：
1948-01-01
影响因子：
--
通讯作者：
HILL, R
中科院分区：
文献类型：
--
作者：
HILL, R
本文提出了一种在宏观尺度上描述各向异性金属的屈服和塑性流动的理论。所考虑的各向异性类型是由择优取向引起的。一个屈服准则是假设一般的理由，这是类似的形式，各向同性金属的Huber-Mises准则，但其中包含六个参数指定的各向异性状态。利用von Mises（1928）的塑性势的概念，在应力和应变增量张量之间找到了相关的关系。该理论被应用于Körber和霍夫（1928）关于从轧制板上切下的薄带在单轴拉伸下的颈缩的实验。它示出，与实验数据完全一致，一般有两个，同样可能的，颈缩方向，其取向取决于带轴和轧制方向之间的角度。作为第二个例子，薄壁圆筒的纯扭转进行了分析。随着捻度的增加，各向异性发展。根据斯威夫特（1947）最近的观测，该理论预测了圆柱体长度的变化。该理论也被应用于确定从轧制板深冲杯形件的制耳位置。
A theory is suggested which describes, on a macroscopic scale, the yielding and plastic flow of an anisotropic metal. The type of anisotropy considered is that resulting from preferred orientation. A yield criterion is postulated on general grounds which is similar in form to the Huber-Mises criterion for isotropic metals, but which contains six parameters specifying the state of anisotropy. By using von Mises’ concept (1928) of a plastic potential, associated relations are then found between the stress and strain-increment tensors. The theory is applied to experiments of Körber & Hoff (1928) on the necking under uniaxial tension of thin strips cut from rolled sheet. It is shown, in full agreement with experimental data, that there are generally two, equally possible, necking directions whose orientation depends on the angle between the strip axis and the rolling direction. As a second example, pure torsion of a thinwalled cylinder is analyzed. With increasing twist anisotropy is developed. In accordance with recent observations by Swift (1947), the theory predicts changes in length of the cylinder. The theory is also applied to determine the earing positions in cups deep-drawn from rolled sheet.