Prediction of Crack Initiation Direction and Fatigue Crack Growth ...

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Deptt. of Mechanical Engineering, College of Technology ... The majority of the research done in the area of fracture mechanics was accomplished in the ...
PREDICTION OF CRACK INITIATION DIRECTION AND FATIGUE CRACK GROWTH UNDER MIXED MODE LOADING Dr Anadi Misra V. K. Singh Associate Professor Associate Professor Deptt. of Mechanical Engineering, College of Technology G. B. Pant University of Agriculture & Technology Pantnagar -263145, INDIA Mail I.D: [email protected]

D. K. Rao M. Tech Scholar

ABSTRACT: The present investigation has been under taken keeping in mind some of the problems concerning the crack propagation direction and growth under constant amplitude load in an inclined crack geometry. The present studies mainly focus on to develop and modified the crack growth criterion to account of the effect of biaxial factor, shearing loading and number of stress terms for different criterion. The effect of one, two and three solution on crack initiation angle determined on the basis of DET-criterion & MTS-criterion. It is seen that difference in crack initiation angle ( α ) obtained from two and three term solution of DET-criterion & MTScriterion is significant and higher than one term solution. The comparisons of predicted result obtain from using DET-criterion and MTS-criterion has been made. When comparison is made between two terms solution, it is found that growth rate is higher in case of DET-criterion than MTS-criterion when α 450. It is observed that only three terms are sufficient to determine the stress and displacement field ahead of the crack tip. Variation of crack initiation angle with crack angle for different biaxial load factor and shear load factor by DET-criterion and MTS-criterion for three term solution is compared. The crack initiation angle also depends upon biaxial factor and shear load factor. NOTATIONS: β = crack inclination angle β 0 = crack initiation angle 2a = Initial crack length r and θ = polar coordinate of crack tip K I , K II = mode I and mode II stress intensity factor σ x , σ y ,τ xy = stress components b1 = Biaxial factor b2 = Shear or torsional load factor INTRODUCTION: Fracture mechanics has been established as an important principle dealing with the growth of fatigue crack. During recent years, the fracture mechanics has obtained a considerable importance for studding the crack growth behavior under static and fatigue loading. The majority of the research done in the area of fracture mechanics was accomplished in the opening mode only. Hence the practical application of the fracture mechanics is limited. The mixed mode crack growth problem has drawn comparably little attention, but is actually more realistic and possibly more dangerous than mode-I crack. The mixed mode growth occurs when a fatigue crack is nucleated along the inclusions or welded defects located making an angle with the axis of the applied load. The fatigue crack growth under multi axial stress is to be considering as mixed mode. The mixed mode cracks generally propagate in a nonself similar manner. Hence, in case of mixed mode loading condition, the study of the crack initiation angle and crack growth rate is of equal importance. A considerable amount of the work has been done to define governing mixed mode loading and crack growth behavior. Papadopoulos (1987) proposed the DET-criterion is based on determinants of the stress tensor. Using the stress as parameter, MTS- criterion proposed by Erdigan & Sih (1963) is based on the

assumption that the material behaves ideally brittle. The theoretical results obtained for different loading cases are shown and discussed by Khan et. al. (2000). Prais (1963) co-relate the rate of crack growth to the stress intensity factor for simple opening (modeI). Robert and Kibla (1971) indicated in their result that the fatigue crack under mixed loading grew in a manner which did not reduce the mode-II component of load to zero and that the growth rate was accelerating by mode-II components of the stress applied simultaneously. ANALYSIS OF THE PROBLEM: Determination of Crack Growth and crack initiation angle DET Criterion and MTS Criterion have been modified by incorporating two and three terms of the stress solutions. Equations for the fracture criterion have been obtained and presented here. DET Criterion states that when the crack initiation starts when the determinant of stress tensor reaches the maximum value. Mathematically, it can be expressed as ∂D ∂2D and …...............(1) θ =θ 0 = 0 θ =θ 0 < 0 ∂θ ∂θ 2 where D= determinant of stress tensor = det σ ij = σ xxσ yy − σ 2 xy … ...............(2) MTS-criterion is widely used due to its simplicity. It is proposed by Erdogan & Sih. It states that crack propagation starts from the crack tip along the radial direction θ = θ 0 ,on which the tangential stress σ θθ , becomes maximum and fracture starts when the maximum tangential stress reaches a critical value, equal to fracture stress in uniaxial tension. Mathematically, it can be expressed as ∂σ θθ ∂ 2σ θθ ..................(3) = 0, and