A split birefringent coating technique to determine dynamic stress intensity factors

2006

Exp Mech

A detailed analytical and experimental investigation is presented to understand the dynamic fracture behavior of functionally graded materials (FGMs) under mode I and mixed mode loading conditions. Crack-tip stress, strain and displacement fields for a mixed mode crack propagating at an angle from the direction of property gradation were obtained through an asymptotic analysis coupled with a displacement potential approach. This was followed by a comprehensive series of experiments to gain further insight into the behavior of propagating cracks in FGMs. Dynamic photoelasticity coupled with high-speed photography was used to obtain crack tip velocities and dynamic stress fields around the propagating cracks. Birefringent coatings were used to conduct the photoelastic study due to the opaqueness of the FGMs. Dynamic fracture experiments were performed using different specimen geometries to develop a dynamic constitutive fracture relationship between the mode I dynamic stress intensity factor (K ID ) and crack-tip velocity ( : a ) for FGMs with the crack moving in the direction of increasing fracture toughness. A similar : a -K ID relation was also obtained for matrix material (polyester) for comparison purposes. The results obtained show that crack propagation velocities in FGMs were about 80% higher than the polyester matrix. Crack arrest toughness was found to be about 10% lower than the value of local fracture toughness in FGMs.

Section: Birefringent Coatingsmentioning

confidence: 99%

Mixed Mode Dynamic Fracture in Particulate Reinforced Functionally Graded Materials

Jain

2006

Exp Mech

“…Asymptotic expansion of crack tip fields. At this point, we employ the standard asymptotic analysis proposed in [Freund 1990]. We introduce coordinates η 1 = x/ε, η 2 = y/ε, where ε is a small arbitrary positive parameter (0 < ε < 1), used so that the region around the crack tip is expanded to fill the entire region of observation.…”

Section: Elastodynamic Transient Crack Tip Fieldsmentioning

confidence: 99%

“…In this study we use a split birefringent coating technique [Der and Barker 1978], in which the coating is placed on both sides of the specimen, and a small distance (2 mm) away from the anticipated crack path. Birefringent coatings consisted of 3 mm thick polycarbonate sheets with vacuum deposited aluminum on the back surface.…”

Section: Birefringent Coatingsmentioning

confidence: 99%

“…A fundamental understanding of the mechanics of crack formation, initiation, and growth is essential for efficient design of critical components fabricated using FGMs. Several researchers have investigated the behavior of embedded and edge cracks in graded materials subjected to quasistatic loading [Jin and Noda 1994;Erdogan 1995;Gu and Asaro 1997;Chalivendra et al 2003;. All these studies concluded that the inverse square-root singularity at the crack tip is not affected by material nonhomogeneities as long as the elastic modulus and Poisson's ratio are sufficiently smooth functions of spatial position.…”

Section: Introductionmentioning

confidence: 99%

“…The transient elastodynamic solution for a crack growing in an arbitrary direction in FGMs is still not known. However, the solution for a homogeneous material is presented in the work of [Freund and Rosakis 1992].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Asymptotic analysis and reflection photoelasticity for the study of transient crack propagation in graded materials

Jain

2007

JOMMS

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 inhouse. 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.

Dynamic Crack Propagation in Particle Reinforced Nanocomposites and Graded Materials

Fracture of Nano and Engineering Materials and Structures

An experimental investigation has been conducted to evaluate the mechanical properties of novel materials fabricated using nano and micron sized particles in polymer matrix. Experiments were also conducted to investigate the dynamic crack propagation in theses particle reinforced materials. High-speed digital imaging was employed along with dynamic photoelasticity to obtain real time, full-field quantification of the dynamic fracture process. Birefringent coatings were used to conduct the photoelastic study due to the opaqueness of these materials [1].Unsaturated polyester resin specimens embedded with small loadings of 36 nm average diameter TiO 2 particles were fabricated using a direct ultrasonification method to study the effects of nanosized particles on nanocomposite bulk mechanical properties [2]. The ultrasonification method employed produced nanocomposites with excellent particle dispersion as verified by TEM. The presence of the particles had the greatest effect on fracture toughness. Both static and dynamic fracture toughness showed marked improvements with addition of small volume fractions (up to 1%)of nano particles. Dynamic fracture experiments were conducted with various specimen geometries to study the complete history of dynamic crack propagation from initiation to crack branching. Results from several of these experiments were compiled in order to establish a relationship between dynamic stress intensity factor, K I , and crack tip velocity, , and the behavior of the nanocomposites is compared with that of the virgin polyester matrix. This relationship is shown in Fig. 1. The specimens used in this study and the nano-particle distribution is also shown in the figure. Crack arrest toughness increased by 64% in the nanocomposite relative to the virgin polyester. Also, Crack propagation velocities in nanocomposites were found to be 50% greater than those in the virgin polyester A detailed analytical and experimental investigation has also been conducted to understand the behavior of a rapidly moving crack-tip in functionally graded materials (FGMs). First, an a