To analyze the stress of functionally graded materials (FGMs) through an experiment, transparent homogeneous FGMs (THFGMs) with similar theoretical and physical properties need to be created. This study developed such THFGMs and proposed a method for determining their stress intensity factors (SIFs) and T-stresses via photoelastic experiments. The Young’s modulus and Poisson’s ratio of these THFGMs linearly change along the physical variation direction, and the shear modulus varies almost linearly. The SIFs and T-stresses were obtained for the central and edge cracks in finite rectangular FGM plates with linear variations in the shear modulus under constant density along the direction of the crack under mode I loading. The SIFs and T-stresses can be obtained using the exponential and linear variation in the stress fields, even if the physical properties of FGM plates show linear variation in the shear modulus. The characteristics of the experimental SIFs obtained in this study generally agree with those of theoretical SIFs reported in previous research. For center crack tips, the SIFs at the hard right crack tip were greater than those at the soft left crack tip. For edge crack tips, when a/W < 0.35, the SIFs were lower than the homogeneous materials. By contrast, when a/W > 0.35, the SIFs were greater than the homogeneous materials. The experimental T-stresses for the center crack agreed well with the numerical T-stresses reported in previous research. For the edge crack, when a/W ≤ 0.3, the experimental T-stresses agreed with the numerical T-stress, but when a/W ≥ 0.4, considerable differences were observed between the experimental and numerical T-stresses. Where a(a) denotes the crack length for edge cracks or half the crack length for center cracks, and W is the width of the specimen. Experimental results coincide well with those reported in the literature, except for the T-stresses for edge crack when a/W > 0.3. Therefore, the THFGMs, which are new FGMs developed in this study, can be effectively used in experimental fracture analysis.

为了通过实验分析功能梯度材料 (FGM) 的应力，需要创建具有相似理论和物理特性的透明均质 FGM (THFGM)。本研究开发了此类 THFGM，并提出了一种通过光弹性实验确定其应力强度因子 (SIF) 和 T 应力的方法。这些 THFGM 的杨氏模量和泊松比沿物理变化方向线性变化，剪切模量几乎呈线性变化。获得了有限矩形 FGM 板中中心和边缘裂纹的 SIF 和 T 应力，在模式 I 加载下，剪切模量在恒定密度下沿裂纹方向呈线性变化。可以使用应力场中的指数和线性变化获得 SIF 和 T 应力，即使 FGM 板的物理特性显示剪切模量的线性变化。本研究中获得的实验 SIF 的特征与先前研究报告的理论 SIF 的特征基本一致。对于中心裂纹尖端，坚硬的右侧裂纹尖端的 ​​SIF 大于柔软的左侧裂纹尖端的 ​​SIF。对于边缘裂纹尖端，当 a/W < 0.35 时，SIF 低于均质材料。相比之下，当 a/W > 0.35 时，SIF 大于均质材料。中心裂纹的实验 T 应力与先前研究中报告的数值 T 应力一致。对于边缘裂纹，当 a/W ≤ 0.3 时，实验 T 应力与数值 T 应力一致，但当 a/W ≥ 0.4 时，观察到实验 T 应力和数值 T 应力之间存在相当大的差异。a ) 表示边缘裂纹的裂纹长度或中心裂纹的裂纹长度的一半，W 是试样的宽度。实验结果与文献报道的结果非常吻合，除了当 a/W > 0.3 时边缘裂纹的 T 应力。因此，本研究开发的新型 FGM THFGM 可以有效地用于实验断裂分析。