Microstructure Lectures

Table of Contents:

1. Introduction
2. Cracks: Atomistic - at Interfaces - in a Continuum
3. Cracks Near Interfaces Between Dissimilar Isotropic Materials
4. Introduction to Mechanical Behavior of Anisotropic Laminates
   • 4.1 Introduction to Mechanical Behavior of Anisotropic Materials
   • 4.2 Introduction to Mechanical Behavior of Laminates
5. Laminate Singularities Caused by Anisotropy: "Free-Edge Problem"
6. Laminate Singularities Caused by Ply Cracks
7. Cracks Near Interfaces Between Dissimilar Anisotropic Materials
   ------ Extension to a Homogeneous Continuum ------

8. Cracks in Homogeneous Isotropic Materials
9. Cracks in Homogeneous Anisotropic Materials
10. Wave Propagation in Homogeneous Isotropic/Anisotropic Materials
11. References

• Interactive Computer Program: Predict stresses in a [0/90/45/-45]_s thin laminate
• Interactive Computer Program: Predict stresses in a [0/90/+45/-45]_s thick laminate prior to 90 ply crack
• Interactive Computer Program: Predict stresses in a [0/90/+45/-45]_s thick laminate near a 90 ply crack

• Case study on influence of ply-cracks on [0/90/+45/-45]s laminate fracture strength:
  Compares stress analysis (FEM program) with fractographs and statistical analysis of fracture strengths.

Stress Analysis Summary: Details of the stress analysis is given in Ref.[1]. Here we show a schematic of the laminate and finite element mesh that was used to model a 90^o ply crack in a [0/90/+45/-45]_s laminate and the stress gradients ("concentrations") in the load bearing 0^o degree ply near the ply crack tip, see also Figures 3 and 4.

Figure 36. Schematic and FEM Grid of Ply Crack in a [0/90/+45/-45]_s laminate, Ref.[1]

Figure 37. Mode I stresses in the 0 degree load bearing ply above the ply crack, Ref.[1].

Summary: With the interactive computer program the reader can vary properties at the microscale and observe the effect these changes have on the stress distributions near the ply crack for two different types of quasi-isotropic laminates. Studying different laminates would require creating different FEM meshes. Future examples will target interactive FEM mesh generation. With this interactive computer program the reader can reproduce these results and study how variations on elastic properties and other properties at the microscale can influence the macroscopic stress state and influence laminate fracture.

Similar to the stress "Free-Edge" FEM problem in section 5.0, the FEM model above predicts stress singularities near the crack tip of a 90^o ply crack in a eight-layered type-II quasi-isotropic laminate. Below we introduce a FEM model with a 90^o ply crack in a [0/90]s laminate with and without a woven macro-structure, Kriz Ref.[23]. These FEM models are complete where stresses plotted in Ref.[23] are reproduced here, but graphical plots of these stress gradients are not shown here because the interactive NPIB modules are under construction.

• Interactive Computer Program: Experiment with lamina stress in a [0/90/]s laminate prior to 90 ply crack
• Interactive Computer Program: Experiment with singularities in a [0/90]s laminate near a 90 ply cracks

• Interactive Computer Program: Experiment with stresses in a 0/90 woven laminate prior to fill crack
• Interactive Computer Program: Experiment with stresses in a 0/90 woven laminate near a fill crack