Nitesh Jain

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 ( ${\mathop a\limits^ \cdot }$ ) for FGMs with the crack moving in the direction of increasing fracture toughness. A similar ${\mathop a\limits^ \cdot }$ -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.

Crack tip stress, strain and displacement fields for a propagating crack along the direction of property gradation in functionally graded materials (FGMs) are obtained through an asymptotic analysis coupled with a displacement potential approach. The analysis for the opening mode is performed assuming two types of property variation: (a) linearly varying shear modulus with constant density, and (b) exponentially varying shear modulus and density. The first six terms in the series expansion of the stress, strain and displacement fields for the dynamic crack are derived to explicitly bring out the influence of nonhomogeneity on the structure of the displacement, strain and stress fields. The analysis revealed that crack tip stress fields retain the inverse square root singularity and only the higher order terms in the expansion are influenced by material inhomogeneity. Using these stress, strain and displacement fields, contours of constant maximum shear stress, constant first stress invariant and constant in-plane displacements are generated and the effect of the nonhomogeneity parameter on these contours is discussed.

Abstract:  This article presents a review of dynamic fracture studies on functionally graded materials. A brief literature review on the fracture mechanics of graded materials is presented first. This is followed by a discussion on the higher-order asymptotic analysis of the transient elastic field surrounding the tip of a dynamically growing crack in a functionally graded material. A comprehensive experimental study of dynamic crack growth in model functionally graded material using the optical method of reflection photoelasticity and high-speed photography is then presented. The results are analysed to establish a generalised relationship between the crack velocity and the dynamic mode-I stress intensity factor (SIF). This relationship is found to be unique and is distinctly different from that previously established for the matrix material (polyester). Finally, an innovative experimental procedure is used to demonstrate the necessity of employing a fully transient stress-field representation in the analysis of optical data for an accurate prediction of the dynamic SIF history.

The dynamic fracture behavior of polyester/TiO2 nanocomposites has been characterized and compared with that of the matrix material. A relationship between the dynamic stress intensity factor,K I and the crack tip velocity,å, has been established. Dynamic photoelasticity coupled with high-speed photography has been 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 nanocomposites. Single-edge notch tension and modified compact tension specimens were used to obtain a broad range of crack velocities. Fractographic analysis was conducted to understand the fracture process. The results showed that crack arrest toughness in nanocomposites was 60% greater than in the matrix material. Crack propagation velocities prior to branching in nanocomposites were found to be 50% greater than those in polyester.

Ongoing with the newer developments in laparoscopic radical prostatectomy (LRP), we report our experience in a consecutive series of 42 patients with a mean 18-month follow-up. We also studied the use of a low-energy source, especially in the region of the prostatic apex and the neurovascular bundle and evaluated its outcome on continence and potency. Between November 2003 and December 2008, 50 patients aged 50-80 yrs underwent LRP with vesicourethral anastomosis and of these, 42 patients who had a minimum follow-up of 3 months were selected for the study. Of these, the initial 16 patients were operated by the routine method and the 26 patients operated in the later part of our experience were operated upon using a minimal energy source. The mean follow-up was 18 months (range 3-60). Continence was evaluated at 1, 3, 6, and 12 months. Eleven of the 16 patients in Group I were continent as compared with 21 of 26 patients in Group II. The difference in continence rates was mainly due to less use of electrocautery and harmonic scalpel at the bladder neck. Of the eight patients who were potent pre-operatively in Group I, four remained potent 3 months after LRP. In Group II, 20 of the 26 patients were potent pre-operatively and 16 remained potent 3 months after LRP. Use of a low-energy source at the bladder neck and neurovascular bundle, sparing of seminal vesicle, and leaving behind a long, healthy stump of the urethra during apical dissection, is associated with better continence and potency without compromising oncological outcome.