Vol. 2, No. 4, 2007

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ISSN: 1559-3959
Asymptotic analysis and reflection photoelasticity for the study of transient crack propagation in graded materials

Nitesh Jain and Arun Shukla

Vol. 2 (2007), No. 4, 595–612
Abstract

The behavior of a rapidly moving transient crack in functionally graded materials (FGMs) is investigated theoretically and experimentally. First, a systematic theoretical analysis is presented for the development of the transient elastodynamic local stress, strain, and displacement field expansions near a growing mixed mode crack tip in FGMs. The crack propagation direction is assumed to be inclined to the direction of the property variation. The displacement potential approach in conjunction with asymptotic analysis is utilized to derive explicit expressions for stress, strain, and in-plane displacement fields. The transient crack growth is assumed to include processes in which both the crack tip speed and the dynamic stress intensity factor are differentiable functions of time. These stress fields are used to generate the contours of constant maximum shear stress (isochromatics fringes) and the effect of transient crack growth on these contours is discussed. To further understand the transient crack growth behavior, a series of dynamic fracture experiments are performed with functionally graded material fabricated in-house. The phenomenon of transition from a static crack to a dynamic mode I crack is examined in these experiments. The full-field stress data around the crack is recorded using dynamic photoelasticity and high-speed digital photography. Due to opaqueness of FGMs, birefringent coatings are employed to obtain the full-field isochromatics around the crack tip. The stress field expansions developed in the first part of the study are used to interpret the experimental observations. The results of the experiments showed that the higher order transient expansion provides an accurate representation of crack tip fields under severe transient conditions.

Keywords
functionally graded material, dynamic fracture, transient crack, asymptotic analysis, photoelasticity, high-speed imaging
Supplementary material

PDF file: Expressions for stress, strain and displacement fields

Milestones
Received: 27 July 2006
Accepted: 23 September 2006
Published: 1 June 2007
Authors
Nitesh Jain
Corporate Research
The Goodyear Tire and Rubber Company
142 Goodyear Blvd.
Akron, OH 44305
United States
Arun Shukla
Dynamic Photomechanics Laboratory
Department of Mechanical Engineering and Applied Mechanics
University of Rhode Island
110 Wales Hall
92 Upper College Rd.
Kingston, RI 02881
United States