# Gradient effects on the fracture of inhomogeneous materials

## Abstract

Functionally Graded Materials (FGMs) have a spatial variation in physical properties that can be tailored to meet the needs of a specific application and/or to minimize internal stresses arising from thermal and elastic mismatch. Modeling these materials as inhomogeneous continua allows assessment of the role of the gradient without requiring detailed knowledge of the microstructure. Motivated by the relative difficulty of obtaining analytical solutions to boundary value problems for FGMs, an accurate finite-element code is developed for obtaining numerical planar and axisymmetric linear thermoelastic solutions. In addition an approximate analytical technique for mapping homogeneous-modulus solutions to those for FGMs is assessed and classes of problems to which it applies accurately are identified. The fracture mechanics analysis of FGMs can be characterized by the classic stress intensities, KI and KII, but there has been scarce progress in understanding the role of the modulus gradient in determining fracture initiation and propagation. To address this question, a statistical fracture model is used to correlate near-tip stresses with brittle fracture initiation behavior. This describes the behavior of a material experiencing fracture initiation away from the crack tip. Widely dispersed zones of fracture initiation sites are expected. Finite-length kinks are analyzed to describe the crackmore »

- Authors:

- Univ. of California, Berkeley, CA (United States)

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 764395

- Report Number(s):
- LBNL-45934

R&D Project: 511906; TRN: AH200102%%142

- DOE Contract Number:
- AC03-76SF00098

- Resource Type:
- Thesis/Dissertation

- Resource Relation:
- Other Information: TH: Thesis (Ph.D.); Submitted to University of California, Berkeley, CA (US); PBD: 1 May 2000

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; ANALYTICAL SOLUTION; BOUNDARY-VALUE PROBLEMS; CRACK PROPAGATION; FRACTURE MECHANICS; FRACTURE PROPERTIES; MICROSTRUCTURE; STRESSES; MATERIALS; FRACTURE FUNCTIONALLY GRADED MATERIALS

### Citation Formats

```
Becker, Terrence Lee.
```*Gradient effects on the fracture of inhomogeneous materials*. United States: N. p., 2000.
Web. doi:10.2172/764395.

```
Becker, Terrence Lee.
```*Gradient effects on the fracture of inhomogeneous materials*. United States. doi:10.2172/764395.

```
Becker, Terrence Lee. Mon .
"Gradient effects on the fracture of inhomogeneous materials". United States. doi:10.2172/764395. https://www.osti.gov/servlets/purl/764395.
```

```
@article{osti_764395,
```

title = {Gradient effects on the fracture of inhomogeneous materials},

author = {Becker, Terrence Lee},

abstractNote = {Functionally Graded Materials (FGMs) have a spatial variation in physical properties that can be tailored to meet the needs of a specific application and/or to minimize internal stresses arising from thermal and elastic mismatch. Modeling these materials as inhomogeneous continua allows assessment of the role of the gradient without requiring detailed knowledge of the microstructure. Motivated by the relative difficulty of obtaining analytical solutions to boundary value problems for FGMs, an accurate finite-element code is developed for obtaining numerical planar and axisymmetric linear thermoelastic solutions. In addition an approximate analytical technique for mapping homogeneous-modulus solutions to those for FGMs is assessed and classes of problems to which it applies accurately are identified. The fracture mechanics analysis of FGMs can be characterized by the classic stress intensities, KI and KII, but there has been scarce progress in understanding the role of the modulus gradient in determining fracture initiation and propagation. To address this question, a statistical fracture model is used to correlate near-tip stresses with brittle fracture initiation behavior. This describes the behavior of a material experiencing fracture initiation away from the crack tip. Widely dispersed zones of fracture initiation sites are expected. Finite-length kinks are analyzed to describe the crack path for continuous crack growth. For kink lengths much shorter than the gradient dimension, a parallel stress term describes the deviation of the kinking angle from that for homogeneous materials. For longer kinks there is a divergence of the kink angle predicted by the maximum energy release rate and the pure opening mode criteria.},

doi = {10.2172/764395},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2000},

month = {5}

}