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S Hasan - One of the best experts on this subject based on the ideXlab platform.

  • Mathematical model for three equal collinear straight cracks: A modified Dugdale approach
    Strength Fracture and Complexity, 2016
    Co-Authors: S Hasan, N Akhtar
    Abstract:

    The present paper discuss a multiple site damage (MSD) problem of three collinear straight cracks exist in an infinite isotropic elastic perfectly Plastic Plate. Uniform stress distribution is applied at the infinite boundary of the Plate in a direction perpendicular to the faces of the cracks. As a result, yield zones are developed ahead each crack tip. These yield zones are sensitive about the load applied at the boundary of the Plate. Since the regions near the crack tips are very week as compared to other parts of the Plate, therefore, it is assumed that the behaviour of yield stress of the Plate near the yield zones is in linear fashion. Hence, rims of the yield zones are subjected to linearly varying stress distribution to stop further opening of cracks along the real axis. The problem is solved using widely used complex variable technique and closed form expressions are derived for stress intensity factor (SIF), crack tip opening displacement (CTOD) and length of developed yield zones at each crack tip. Under small-scale yielding, numerical results for yield zone length and crack-tip opening displacement as a function of remotely applied stress are obtained and presented graphically.

  • application of modified dugdale model to two pairs of collinear cracks with coalesced yield zones
    Applied Mathematical Modelling, 2016
    Co-Authors: S Hasan
    Abstract:

    Abstract In this paper, a modified Dugdale’s approach has been presented to arrest four straight collinear quasi-static cracks with coalesced yield zones. An infinite elastic perfectly Plastic Plate, containing four cracks, is subjected to uniform stresses applied at infinite boundary of the Plate. As a result, yield zones develop at each crack tip. On increasing the stresses, yield zones between two pairs of cracks get coalesced and after that at each internal crack tip. In order to detain propagation of cracks, a quadratic yield stress distribution is applied on the rims of the yield zones. This distribution enables to investigate the residual strength of an infinite Plate, when the Plate fails at a stress which is well below the yield stress of the Plate. Muskhelishvili’s complex variable technique is use to solve the stated problem. Analytical expressions for stress intensity factor and crack-tip opening displacements are established. The results validate with previously published works.

  • DUGDALE MODEL FOR THREE UNEQUAL COLLINEAR STRAIGHT CRACKS WITH COALESCED YIELD ZONES: A COMPLEX VARIABLE APPROACH
    International journal of pure and applied mathematics, 2015
    Co-Authors: S Hasan
    Abstract:

    The paper aims to provide an analytical solution of the problem of three unequal collinear straight cracks with coalesced Plastic/yield zones weakening an infinite elastic perfectly Plastic Plate. These cracks are located on the real axis in such a manner that the two cracks exist very close to each other. Cracks are open in mode-I type deformation on the application of uniform stresses at the infinite boundary of the Plate. Hence, yield zones are developed at each crack tip. Stresses applied at the infinite boundary of the Plate increased to such a limit that the yield zones developed between two closely located cracks are coalesced. Assume that the yield stress of the Plate is enough to detain further opening of cracks. The problem is solved using complex variable method and analytical expressions are derived for stresses applied at infinite boundary of the Plate, yield zone length. A comparative study is carried out for load bearing capacity with the results of two collinear straight cracks, which is the limiting case of the cracks configuration considered in this paper.

  • dugdale model for three equal collinear straight cracks an analytical approach
    Theoretical and Applied Fracture Mechanics, 2015
    Co-Authors: S Hasan, N Akhtar
    Abstract:

    Abstract In the paper, solution of three collinear equal straight cracks has been investigated on the basis of Dugdale’s hypothesis. These cracks damage an infinite isotropic elastic perfectly Plastic Plate. Crack tips are very sensitive about loads applied at the infinite boundary of the Plate. Each crack tip opens in mode-I type deformation on the application of repeated loads at the boundary of the Plate, as a result yield zones develop at each crack tip. To stop further opening of cracks, the rims of the developed yield zones are subjected to yield stress distribution. Muskhelisvili’s complex variable method is used to derive analytical expressions for complex potential function, stress intensity factor (SIF), components of displacement and crack tip opening displacement (CTOD) at each crack tip. Some of the analytical expressions are validated with previously published work. Numerical results are obtained for load bearing capacity, yield zone length and CTOD. These results are analyzed and reported graphically for different cracks lengths.

  • Crack-tip-opening displacement for four symmetrically situated cracks with coalesced interior yield zones
    Applied Mathematical Modelling, 2012
    Co-Authors: R. R. Bhargava, S Hasan
    Abstract:

    Abstract Crack-tip opening displacements are obtained for four collinear straight cracks, weakening an unbounded homogeneous and isotropic elastic-perfectly Plastic Plate. The cracks are so configured that two symmetrically situated and interiorly lying cracks are of equal-lengths. Other two exteriorly lying, collinear straight cracks (surrounding the interiorly lying straight cracks) are of mutually equal-lengths. Thus an exterior and an interior crack-set are symmetrically oriented with respect to the other interior–exterior collinear cracks-set configuration. Uniform constant load prescribed at remote boundary of the Plate, opens the crack in self-similar fashion developing a strip-yield zone ahead each tip of the cracks. It is assumed that the strip-yield zone developed at each of interior tips of an exteriorly and interiorly lying crack-set configuration gets coalesced. The developed yield zones are subjected to normal cohesive yield stress to arrest the crack from further opening. The solution of the problem is obtained by superposing the solutions of the two auxiliary problems, appropriately derived from the given problem. Each of the auxiliary problems, in turn, is solved using complex variable technique. Expressions are derived for quantities of interest viz. crack-tip opening displacement (CTOD), length of each developed yield zone. The effect of applied load and closing load on the parameters CTOD and strip yield zone affecting the crack arrest is presented graphically and concluded.

W J Stronge - One of the best experts on this subject based on the ideXlab platform.

  • deformation of simply supported circular Plate by central pressure pulse
    International Journal of Solids and Structures, 1996
    Co-Authors: Dongquan Liu, W J Stronge
    Abstract:

    Abstract Bending of a circular simply supported Plate subjected to a central pressure pulse is investigated theoretically; the Plate is assumed to be rigid perfectly-Plastic and follows the Tresca yield condition. Results are presented for a central pulse of constant pressure and brief duration. If the blast pressure is sufficiently large the radial bending moment changes sign between the region of loading and the periphery of the Plate. Previous analyses of pulse loading on a simply supported rigid-Plastic Plate gave bending moments that satisfied the yield condition only if the pressure magnitude was not very large. The present analysis extends the previous analyses into the range of large pressures.

R. R. Bhargava - One of the best experts on this subject based on the ideXlab platform.

  • Crack-tip-opening displacement for four symmetrically situated cracks with coalesced interior yield zones
    Applied Mathematical Modelling, 2012
    Co-Authors: R. R. Bhargava, S Hasan
    Abstract:

    Abstract Crack-tip opening displacements are obtained for four collinear straight cracks, weakening an unbounded homogeneous and isotropic elastic-perfectly Plastic Plate. The cracks are so configured that two symmetrically situated and interiorly lying cracks are of equal-lengths. Other two exteriorly lying, collinear straight cracks (surrounding the interiorly lying straight cracks) are of mutually equal-lengths. Thus an exterior and an interior crack-set are symmetrically oriented with respect to the other interior–exterior collinear cracks-set configuration. Uniform constant load prescribed at remote boundary of the Plate, opens the crack in self-similar fashion developing a strip-yield zone ahead each tip of the cracks. It is assumed that the strip-yield zone developed at each of interior tips of an exteriorly and interiorly lying crack-set configuration gets coalesced. The developed yield zones are subjected to normal cohesive yield stress to arrest the crack from further opening. The solution of the problem is obtained by superposing the solutions of the two auxiliary problems, appropriately derived from the given problem. Each of the auxiliary problems, in turn, is solved using complex variable technique. Expressions are derived for quantities of interest viz. crack-tip opening displacement (CTOD), length of each developed yield zone. The effect of applied load and closing load on the parameters CTOD and strip yield zone affecting the crack arrest is presented graphically and concluded.

  • crack arrest model for a Plate weakened by internal and external cracks a modified dugdale approach
    Mechanics of Composite Materials, 2002
    Co-Authors: R. R. Bhargava, P K Bansal
    Abstract:

    A modified Dugdale model solution is obtained for an elastic-perfectly-Plastic Plate weakened by one internal and two external straight collinear hairline cracks. The tension applied to the infinite boundary of the Plate opens the rims of cracks with forming a Plastic zone ahead of each tip of the internal crack and also at each finitely distant tip of the two external cracks. The developed Plastic zones are closed by normal cohesive linearly varying yield-point stress distributions applied to their rims. The problem is solved using the complex-variable technique. A case study is carried out to find the load required to prevent the cracks from further growing with respect to affecting parameters. The results obtained are reported graphically and analyzed.

Dongquan Liu - One of the best experts on this subject based on the ideXlab platform.

  • deformation of simply supported circular Plate by central pressure pulse
    International Journal of Solids and Structures, 1996
    Co-Authors: Dongquan Liu, W J Stronge
    Abstract:

    Abstract Bending of a circular simply supported Plate subjected to a central pressure pulse is investigated theoretically; the Plate is assumed to be rigid perfectly-Plastic and follows the Tresca yield condition. Results are presented for a central pulse of constant pressure and brief duration. If the blast pressure is sufficiently large the radial bending moment changes sign between the region of loading and the periphery of the Plate. Previous analyses of pulse loading on a simply supported rigid-Plastic Plate gave bending moments that satisfied the yield condition only if the pressure magnitude was not very large. The present analysis extends the previous analyses into the range of large pressures.

Yuchin Huang - One of the best experts on this subject based on the ideXlab platform.

  • manufacture of dual side surface relief diffusers with various cross angles using ultrasonic embossing technique
    Optics Express, 2009
    Co-Authors: Shih-jung Liu, Yuchin Huang
    Abstract:

    This paper reports a simple and effective ultrasonic embossing method which enables the rapid fabrication of dual-side surface-relief Plastic diffusers with various cross angles. Metallic master molds bearing microstructures are fabricated using a tungsten carbide turning machine. A 1500-Watt ultrasonic vibrator with an output frequency of 20 kHz was used to replicate the microstructure onto 1 mm thick PMMA and PET films in the experiments. During ultrasonic embossing, the ultrasonic energy is converted into heat through intermolecular friction at the master mold/Plastic Plate interface due to asperities to melt the thermoPlastic at the interface and thereby to replicate the microstructure. Under the proper processing conditions, high-performance dual-sided Plastic diffusers of various cross-angles can be successfully fabricated. The proposed method shows great potential for fast fabrication of micro-optical components due to its simplicity and versatility.