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Introduction to Fracture Mechanics 1 Introduction to Fracture Mechanics From Suresh: Fatigue of Materials INTRODUCTION Importance of Fracture Mechanics :  All real materials contain defects: understand the influence of these defects on the strength of the material. Defect - tolerant design philosophy. 2 the material. Defect - tolerant design philosophy.  Relevance for Fatigue: understand the initiation and growth of fatigue cracks. We will use two approaches, an energy-based approach and a more rigorous mechanics approach. Key Idea : Griffith (1921) postulated that for unit crack extension to occur under the influence of the applied stress, the decrease in potential energy of Griffith Fracture Theory Introduction 3 applied stress, the decrease in potential energy of the system, by virtue of the displacement of the outer boundaries and the change in the stored elastic energy, must equal the increase in surface energy due to crack extension. Consider the center-cracked plate shown below. The in-plane dimensions of the plate are large compared to the crack length. 4 Using the results of Inglis (1913) Griffith found that the net change in potential energy of the plate caused by the introduction of the crack is: . ' 22 E Ba W P   ' E E  5 = E Plane stress The surface energy of the crack system is 2 1 ' v E E   sS aBW  4  Plane strain where γ S is the free surface energy per unit surface area. The total system energy is then given by .4 ' 22 SSP aB E Ba WWU    6 Griffith noted that the critical condition for the onset of crack growth is: ,02 ' 2  S S P E a dA dW dA dW dA dU   where A=2aB is the crack area and dA denotes an incremental increase in the crack area. Thus the stress required to initiate fracture is: . '2 a E S f     7 a  As the second derivative, d 2 U/da 2 is negative, the above equilibrium condition gives rise to unstable crack propagation. This applies for brittle materials; it must be modified for ductile materials such as metals. Orowan (1952) extended Griffith’s brittle fracture concept to metals by simply adding a term representing plastic energy dissipation. The resultant expression for fracture initiation is , )('2E p s     8 , a p s f    where is the plastic work per unit area of surface created. Generally is much larger than p  . s  p  Energy Release Rate Crack Driving Force Consider an elastic plate with an edge crack of length as shown below: , a 9 The total mechanical potential energy of a cracked elastic body is given by the general expression FP wW    where is the stored elastic strain energy and is  F w 10 the work done by the external forces.  F Irwin (1956) proposed an approach for the characterization of the driving force for fracture in cracked bodies, which is conceptually equivalent to that of the Griffith model. . Introduction to Fracture Mechanics 1 Introduction to Fracture Mechanics From Suresh: Fatigue of Materials INTRODUCTION Importance of Fracture Mechanics :  All real materials. rigorous mechanics approach. Key Idea : Griffith (19 21) postulated that for unit crack extension to occur under the influence of the applied stress, the decrease in potential energy of Griffith Fracture. energy due to crack extension. Consider the center-cracked plate shown below. The in-plane dimensions of the plate are large compared to the crack length. 4 Using the results of Inglis (19 13) Griffith