# Strength prediction in composites with stress concentrations: classical Weibull and critical failure volume methods with micromechanical considerations

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## Abstract

Application of Weibull statistics to tensile strength prediction in laminated composites with open holes is revisited. Quasi-isotropic carbon fiber laminates with two stacking sequences [45/0/−45/90]_{s} and [0/45/90/−45]_{s} with three different hole sizes of 2.54, 6.35 and 12.7 mm were considered for analysis and experimental examination. The first laminate showed 20% lower strength for smaller and 10% for the larger hole sizes. A novel critical failure volume (CFV) method with minimum scaling length constraint as well as the traditional Weibull integral method were applied. The strength prediction was based on the state of stress in the 0^{°} ply by taking into account the redistribution of stress due to matrix damage in the form of splitting, delamination and matrix cracking of off axis plies. The state of matrix damage precipitating failure was recorded by using X-radiography and examined by a sectioning technique. The measured extent of damage was then included in a 3D stress analysis procedure by using a mesh independent crack modeling method to account for fiber direction stress redistribution. The CFV method gave results within one standard deviation from experimentally observed strength values for both laminates and all three hole sizes. The Weibull integral method underpredicted the strength in all cases from as much as 20–30% for smaller hole sizes to 8% for the large holes. The accuracy of failure predictions using CFV is attributed to the introduction of a minimum scaling length. This length has a physical meaning of the width of a process zone of formation of fiber macro-crack as a result of single fiber break interaction. Direct measurement or rigorous evaluation of this parameter is, however, difficult. Consistent with referenced micromechanical studies, its value was assigned equal to six times the Rosen’s ineffective length.

### Keywords

Shape Function Hole Size Weibull Modulus Strength Prediction Fiber Failure## Notes

### Acknowledgements

The work was supported by Air Force Research Laboratory through contract number FA8650-05-D-5052 to the University of Dayton Research Institute. The authors are grateful to Chase Nessler of the Southwest Council of Higher Education for performing the sectioning studies.

### References

- 1.ASTM D3039/D3039M-00e2. Standard test method for tensile properties of polymer matrix composites. ASTM International, West Conshoken, PA, December, 2000Google Scholar
- 2.Whitney JM, Nuismer RJ (1974) J Compos Mate 8:253Google Scholar
- 3.Waddoups ME, Eisenmann J and Kaminski BE (1971) J Compos Mater 5:446Google Scholar
- 4.Nuismer RJ, Whitney JM (1975) Fract Mech Compos, ASTM STP 593:117Google Scholar
- 5.Whitney JM, Kim RY (1976) Effect of stacking sequence on the notched strength of laminated composites, AFML-TR-76-177Google Scholar
- 6.Kortshot MT, Beaumont PWR (1990) Compos Sci Technol 39:303CrossRefGoogle Scholar
- 7.Iarve EV (2003) Int J Mth Eng 56:869CrossRefGoogle Scholar
- 8.Iarve EV, Mollenhauer DH, Kim R (2005) Compos Part A 36:163CrossRefGoogle Scholar
- 9.Mollenhauer D, Iarve EV, Kim R, Langley B (2006) Composites: Part A 282:294Google Scholar
- 10.Wismon MR (1999) Compos Sci Technol 59:1937CrossRefGoogle Scholar
- 11.Wisnom MR, Khan B, Green B, Jiang W, Hallet SR (2005) Specimen size effects on tensile strength and failure mechanisms of carbon/epoxy composites. JNC14 Conference, Compiegne, March 2005Google Scholar
- 12.Wu EM (1978) Failure analysis of composites with stress gradients, UCRL-80909Google Scholar
- 13.Wetherhold RC and Whitney JM (1981) Polymer Compos 2(3):112CrossRefGoogle Scholar
- 14.Wetherhold RC (1985) J Compos Mater 19:19Google Scholar
- 15.Iarve EV, Mollenhauer DH, Kim R (2006) Composites Part A (accepted)Google Scholar
- 16.Moes N, Dolbow J and Belytschko T (1999) Int J Numer Methods Eng 46:131CrossRefGoogle Scholar
- 17.Rosen BW (1964) AIAA J 2:1985CrossRefGoogle Scholar
- 18.Landis CM, Beyerlin IJ, McMeeking RM (2000) Mech Phys Solids 48:621CrossRefGoogle Scholar
- 19.Bazant ZP (2002) Scaling of structural strength. Hermes Penton Science (Kogan Page Science), LondonGoogle Scholar
- 20.Pagano NJ, Schoeppner GA, Kim R, Abrams FL (1998) Compos Sci Technol 58:1811CrossRefGoogle Scholar