Microstructure Lectures

by

Ronald D. Kriz, Associate Professor
Engineering Science and Mechanics
Virginia Polytechnic Institute and State University
Blacksburg, Virginia 24061


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
  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

6.0 Laminate Singularities Caused by Ply Cracks: FEM Model

After the formation of a ply crack, see Figure 25, new singularities occur near the ply crack tip. The growth of this crack can continue into the adjacent ply, see Figures 1, 3, 4, and 5, or debond along the interface. Below we provide models that demonstrate how anisotropy and residual stress can augment singularities near ply cracks and influence how ply cracks grow and control laminate fracture strength. In this section we provide:

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


Figure 28. Schematic and FEM Grid of Ply Crack in a [0/90/+45/-45]s laminate


Figure 29. Mode I stresses in the 0 degree load bearing ply above the ply crack.

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 "Free-Edge" problem the model above predicts stress singularities of a ply crack in a eight-layered quasi-isotropic laminate. Below we introduce an FEM model for a simpler [0/90]s laminate with and without a woven macro-structure.

---- UNDER CONSTRUCTION ----


Course content in this section: email Dr. Ron Kriz
http://www.jwave.vt.edu/crcd/kriz/lectures/PlyCracks.html
Created November 1997 / Modified September 17, 2000