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Deformation and fracture of aluminium foams under proportional and non proportional multi-axial loading: statistical analysis and size effect

机译:比例和非比例多轴载荷下泡沫铝的变形和破裂:统计分析和尺寸效应

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摘要

An extensive experimental programme and detailed mechanical analysis were performed to test and model the statistical response of metallic foams under complex loading conditions. Tensile tests were performed on more than 80 specimens of closed-cell aluminium foams with four different specimen sizes. These test results show a large scatter and a significant size effect especially on standard deviation. The average fracture stress and, more significantly, the corresponding scatter decrease for increasing volume sizes. An attempt is made to use the Weibull statistical analysis to interpret these variations. A Weibull modulus close to 8 is found. Compression tests were also carried out. Both mean fracture stress in tension and mean peak stress in compression and the corresponding dispersions are correctly described by a single set of Weibull parameters. The statistical model is extended to multi-axial loading conditions by introducing an effective stress measure involving both the deviatoric part of the stress tensor and its trace. One additional parameter is identified using the average shear yield stress obtained from pure shear tests and torsion tests on solid bars. It is shown that the model is able to predict the dispersion found for the shear strength. Two types of combined tension/compression-torsion loading conditions were then tested experimentally. The non-proportional loading path consists of a tension test followed by torsion, keeping the axial stress constant. In the proportional loading path, shear and axial stress follow a straight line in the stress space. The corresponding surface of average yield/fracture stress is found to be symmetric. The experimental results are in good agreement with the predictions of the statistical model. The model predicts a bell-shaped surface for the first loading path and a quasi-elliptic one for the proportional one. The scatter found in the description of this surface is also accounted for accurately by the model. A brief discussion of an extension of Beremin's micromechanical model to the statistical failure of brittle foams is presented.
机译:进行了广泛的实验程序和详细的机械分析,以测试和模拟复杂载荷条件下金属泡沫的统计响应。拉伸试验是对80种具有四种不同样品尺寸的闭孔铝泡沫样品进行的。这些测试结果显示出较大的散布和明显的尺寸影响,尤其是对标准偏差。随着体积尺寸的增加,平均断裂应力以及更显着的散射减小。尝试使用Weibull统计分析来解释这些变化。发现威布尔模量接近8。还进行了压缩测试。拉伸的平均断裂应力和压缩的平均峰值应力以及相应的色散都可以通过一套威布尔参数来正确描述。通过引入涉及应力张量的偏斜部分及其轨迹的有效应力测量,将统计模型扩展到多轴载荷条件。使用从纯钢筋上的纯剪切试验和扭转试验获得的平均剪切屈服应力确定一个附加参数。结果表明,该模型能够预测剪切强度的离散度。然后通过实验测试了两种组合的拉伸/压缩-扭转加载条件。非比例加载路径包括拉伸测试,然后进行扭转,以保持轴向应力恒定。在比例加载路径中,剪应力和轴向应力在应力空间中遵循一条直线。发现平均屈服/断裂应力的相应表面是对称的。实验结果与统计模型的预测吻合良好。该模型预测第一加载路径的钟形表面和比例加载路径的准椭圆形表面。该表面的描述中发现的散点也可以由模型准确解释。简要讨论了将Beremin的微机械模型扩展到脆性泡沫的统计失效的问题。

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