Fracture Mechanics by Nestor Perez

Author:Nestor Perez
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

5.19. Assume that isotropic solid material having a single-edge crack is subjected to a remote tensile stress at room temperature. Let the properties of the material be σ ys  = 500 MPa, Poisson’s ratio , and E = 72 GPa. Let the applied stress intensity factor for mode I loading be . Excluding microstructural details and microscale defects, use the Tresca yielding criterion to derive (a) an expression for the critical plastic zone angle (θ c ) and its magnitude when minimum principle stresses are equal (σ 2 = σ 3) and (b) determine when σ min = σ 2 and σ min = σ 3 by knowing the value of θ c , (c) the plastic zone size at θ c , and . The Tresca yielding criterion is based on the maximum shear stress reaching a critical or failure level. Hence, the definition of the maximum shear stress for this criterion is , where σ max and σ min are principle stresses and σ ys is the monotonic tensile yield strength of a solid material. Let σ max = σ 1 and σ min = σ 2 or σ min = σ 3.

5.20. Consider a ductile steel plate containing a 50-mm through-thickness central crack subjected to a remote tensile stress of 40 MPa. If the yield strength of the steel is 300 MPa, then calculate as per LEFM, Irwin’s approximation and the Dugdale’s strip yield criterion. Compare results. Repeat all calculations for a 290 MPa remote stress. Explain.

5.21. A single-edge SE(B) specimen with B = 20 mm, w = 40 mm is used to determine the critical CTOD δ tc and J IC . See Example 5.4 for the specimen configuration and the load-displacement plot. Assume plane-strain conditions and let

P max = 38 kN; σ ys  = 800 MPa; E = 207 GPa

; v = 0. 3

B = 20 mm; w = 40 mm; δ p  = 1. 00 mm

S = 150 mm; z = 1. 5 mm; a = 12 mm

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