Many materials with a microstructure are statistically inhomogeneous, like casting skins in polymers or grain size gradients in polycrystals. It is desirable be able to account for the structural gradient. The first step is to measure the location dependent properties, for example by tensile testing of thin slices. Unfortunately, the slices properties can differ significantly from the bulk properties, since the slices lack a scale separation in one direction. For Polypropylen, we measured that Young’s modulus of the slices is approximately 70% of the respective bulk value. We have identified three significant effects, all making the slices appear softer than the bulk material:

• Load path confinement: The approximate plane stress forces the load path through a softer phase where in 3D-of-plane load distribution is possible.

• Free lateral straining: In thin slices, small regions can contract freely, while phases have to contract concurrently in the bulk. Therefore, when two phases have very different Poisson ratios, the bulk appears stiffer than a slice.

• Topological changes upon slicing: Interpenetrating phases in the bulk can show features of a matrix-inclusion-structure in the slices.

We examine and quantify these effects in the linear elastic range for matrix-inclusion-structures and an interpenetrating-phase-structure. Some approaches on how the slice- vs bulk difference can be estimated are given.

许多具有微观结构的材料在统计上是不均匀的，例如在聚合物中浇铸蒙皮或在多晶中形成晶粒尺寸梯度。希望能够考虑结构梯度。第一步是测量位置相关的属性，例如通过对薄片进行拉伸测试。不幸的是，切片的性质可能与块状的性质明显不同，因为切片在一个方向上缺少水垢分离。对于聚丙烯，我们测量到切片的杨氏模量约为各自体积值的70％。我们已经确定了三个明显的效果，所有这些效果都使切片看起来比散装材料更柔软：

• 载荷路径限制：近似的平面应力迫使载荷路径通过一个较软的相，这可能导致3D平面载荷分布。

• 自由的横向应变：在薄片中，小区域可以自由收缩，而相必须在整体中同时收缩。因此，当两个相的泊松比非常不同时，块体看起来比切片更硬。

• 切片时的拓扑变化：本体中的互穿相可以显示切片中基质-包裹体结构的特征。

我们检查和量化这些影响在线性弹性范围内的矩阵包含结构和互穿相结构。给出了一些有关如何估计切片与体积差异的方法。