Materials Science And Engineering Properties
1st Edition
ISBN: 9781111988609
Author: Charles Gilmore
Publisher: Cengage Learning
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Chapter 11, Problem 11.2P
To determine
The length of crack initiated the fracture.
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Failure of engineering materials
A specimen of a 4340 steel alloy with a plane strain fracture toughness of 54.8 MPa is exposed to a stress of 1766 MPa. Assume that the parameter Y has a value of 1.6.If the largest surface crack is 0.5236 mm long, determine the critical stress .
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Chapter 11 Solutions
Materials Science And Engineering Properties
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- A thin plate of a ceramic material with E = 225 GPa is loaded in tension, developing a stress of 450 MPa. Is the specimen likely to fail if the most severe flaw present is an internal crack oriented perpendicular to the load axis that has a total length 0.25 mm and a crack tip radius of curvature equal to 1 μm?arrow_forwardWhich of the following statements regarding brittle failure and crack propagation is CORRECT? Elastic energy is consumed when a crack propagates, due to unloading of a volume of material. Energy is released when the surface area of a material increases, as a result of crack propagation. O The stress at the tip of a crack is less than the nominal stress (force over the cross-sectional area of the component) because the stress flows around the defect. O The fracture toughness of a material is its resistance to an increase in the radius of curvature of a crack. O A material will fail in brittle fashion when the stress intensity at the crack tip is greater than the fracture toughness of the material.arrow_forwardA structural component in the shape of a flat plate 20.8 mm thick is to be made from a metal with yield strength of 533 MPa and a critical fracture toughness of 22.0 MPa-m!2. Assume a crack forms in the plate, and the geometry of the crack yields a Y value of 1.5. If the plate is designed to a design stress equivalent to 0.3 times the yield strength, what is the critical crack length? Equations: 1/2 () Om К = 2 σο K. = YocTa %3D Ptarrow_forward
- A material containing cracks of initial length 0.010 mm is subjected to alternating tensile stresses of 25 and 125 MPa for 350,000 cycles The material is then subjected to alternating tensile and compressive stresses of 250 MPa. How many of the larger stress amplitude cycles can be sustained before failure? The material has a fracture toughness of 25 MPaVm and materials constants of n-3.1 and C-1.8 × 10-1º for these units. Assume f- 1.0 for all cracksarrow_forwardA very large, steel plate of yield stress 200 MPa and Poisson's ratio 0.3 has a crack at the centre of length 34 mm, orientated along the x-axis. If the plate is subjected to far field tensile loading of magnitude 177 MPa and is assumed to be in a state of plane stress, determine the extent of the plastic region at the crack tip, along the x-axis. You may assume Poisson's ratio is (1/3). Express your answer as an integer value of mm.arrow_forwardThe (G-E) diagram obtained in the tensile test performed on a metal sample with a diameter of 16 mm is as follows. The loads at points A, B and C and the elongation measured on l. 16 cm gauge length were determined as follows: B A B C Load (kgf) 4800 8400 7200 Elongation (mm) 0.192 28.8 38.4 c) Calculate the fracture work and the maximum elastic energy the metal rod can store. d) Find the cross-sectional area of a 6 m long rod made of this metal such that it can carry 12 tons of load with 2 times the safety of yield strength. How long does the rod extend under this load?arrow_forward
- The limit load of an elastic-plastic cracked three-point bend beam (Figure QA1) with S = 4W = 120 mm, crack length a and a/W = 0.4 is (PL)c. Calculate %3D the crack opening stress at a distance of 0.5 mm ahead of the crack tip in an elastic specimen subjected to bending load equal to the limit load. Assume that the materials yield strength is equal to oy 300 MPa and the specimen is under plane strain condition. Figure QA1: three-point bend beam P. SIarrow_forwardA very large, steel plate of yield stress 200 MPa has a crack at the centre of length 18 mm, orientated along the x-axis. If the plate is subjected to far field tensile loading of magnitude 179 MPa and is assumed to be in a state of plane strain, determine the extent of the plastic region at the crack tip, along the x-axis. You may assume Poisson's ratio is (1/3). Express your answer as an integer value of mm.arrow_forwardcompare the effect of presence of a notch on ductile and brittle materials in terms of fracture behaviourarrow_forward
- 2. a) As an engineer, choose a desired fracture mode in metals with one (1) reason. b) Sketch the fracture behaviour in metals. c) i. The modulus of elasticity of a metal alloy A is 260 GPa. Compute the specific surface energy if propagation of an internal crack of length 0.40 mm is observed when a stress of 63 MPa is applied to the alloy. ii. The elastic deformation energy of alloy A is 3.0 J/m². Based on the answer obtained in c)(i), show whether alloy A is an elastic deformation or a plastic deformation. iii. Interpret if alloy A can be classified as a brittle or a ductile material. d) i. A metal with an internal crack is loaded with a tensile stress of 15 MPa. If the crack length and the radius of curvature are 2.6 x 10-2 mm and 1.1 x 10-4 mm, compute its maximum stress. ii. The modulus of elasticity of the metal is 90 GPa and the specific surface energy is 2.6 J/m2. Based on its critical stress, show that the crack will not grow when a tensile stress of 15 MPa is loaded on it.arrow_forward2- What is the largest size (mm) internal through crack that a thick plate of aluminium alloy 7075-T651 can support at an applied stress of (a) three-quarters of the yield strength and (b) one-half of the yield strength? Assume Y = 1. for 7075-T651, KỊC = 24.2 MPa ym and oYS = 495 MPa.arrow_forwardQ1/ For through thickness elliptical crack in an infinite Plate, the tensile stress distribuction ahead of the crack tip is accurately described by the equation 6- 6 nom when X = 1.02 a.in terms of stress intensity factors the tip can be approximated crack What is the as 6 K √6.48 difference between the stress distribution of these two. equations at a distance r= 0.02 a ahead of the crack tip?arrow_forward
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