Derive an expression for the toughness of a material whose stress-strain relationship is defined by the relationship o K(ɛ + 0.2)". Here K and n are constants, and we denote the fracture
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- 1. For the stress-strain curve shown below, please estimate the properties indicated. (a) Fracture Strain Please do your work on a separate sheet of paper, and put your answers in the boxes on the right. Be sure to include the proper symbol and units. Stress Strain 70 60 50 Stress (ksi) 240 30 20 10 70 0 0.000 60 50 Stress (ksi) 40 20 10 KULL 0 0.000 0.010 0.050 0.100 Strain (in/in) Stress Strain 0.020 0.030 Strain (in/in) 0.040 0.150 0.050 (b) Ultimate Tensile Stress (c) Fracture Stress (d) Proportional Limit (e) Elastic Modulus (1) Yield Stress (g) Tensile Toughness (Modulus of Toughness) (h) Modulus of ResilienceEstimate the theoretical fracture strength of a brittle material if it is known that fracture occurs by the propagation of an elliptically shaped surface cra of length 0.5 mm and having a tip radius of curvature of 0.005 mm, when a stress of 1040MPa is applied. Your answer must be in GPa. Write your answer to 1 decimal place. Answer: V 30 (0) 00 a W 4340 steel alloy. Determine the ductile to brittle transitionA specimen of a steel alloy with a plane strain fracture toughness of 22.1 MPavm. The largest surface crack is 0.6 mm long? Assume that the parameter Y has a value of 0.5. What is the critical stress in MPa. Write your answer with 2 decimal places. Answer: 0 dºvo vo (0) 00 00, GM
- QUESTION 2 (a) Stress and strain diagram of 316L stainless steel is plotted in Figure Q2 (a). Determine and label the following terms: (i) Proportional limit point (0,ɛ) (ii) Yield point (0,ɛ) (iii) Ultimate point (0,8) (iv) Fracture point (0,8) (iv) Modulus of elasticity or Young's modulus (E) 700 400 600 500 300 400 200 6 300 200 E 100 100 0.005 0.01 0.015 0.02 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 Strain, E (mm/mm) Strain, E (mm/mm) Figure Q2 (a) (b) A short post AB constructed from a hollow circular tube of aluminium, supports a compressive load of 116 kN as in Figure Q2 (b). The inner and outer diameters of the tube are di=100 mm and dz=112 mm, respectively, and its length is 400 mm. The shortening of the post due to the load is measured as 0.3 mm. Determine the compressive stress and strain in the post. Note: the weight of the post is neglected. 116 KN A 400 mm Figure Q2 (b) Stress, o (MPa) Stress, a (MPa)Consider the engineering stress-strain curves for three materials labeled A, B, and C below. Qualitatively, put the materials in the order in terms of largest-to- smallest strain hardening and Ductility. Stress B StrainFor a piece of copper alloy, a standard stress test was applied to it, the following data was collected, from which a stress-strain diagram must be generated, where as data it is known that the initial diameter of the element is 0.505in. The analysis must include the following: 1.Modulus of Elasticity and modulus of resilience. 2.Percentage of elongation. 3.Percentage of area reduction. 4.Real and engineering stress at fracture. It is known that after the specimen fractures, its dimensions in terms of length and diameter are 3.014 and 0.374in, respectively.
- Consider a cylindrical specimen of a steel alloy with 8.5 mm diameter and 80 mm long that is pulled in tension. Estimate the following mechanical properties using Fig. 1: a. Modulus of Elasticity and Resilience in MPa and psi b. Ultimate Tensile Strength in MPa and psi c. Fracture Strength in MPa and psi d. Ductility or % elongation at fracture in MPa and psi 2000 10³ psi MPa 300 2000 200 1000 100 0 0.000 0.005 0.010 0.015 Strain 0.020 0.040 0.060 Strain Fig. 1 Engineering Stress-Strain Curve Stress (MPa) 1000 0 0.000 Stress 0.080 300 200 100 0 Stress (10³ psi)Use the engineering stress strain diagram provided below to answer parts (A) to (H) below (the stress-strain diagram bas already been drawn for you): stress strain diagram 400 350 0 300 0 250 0 200 0 150.0 100.0 50.0 O 05 0 1 0.15 strain A. Determine the tensile strength of this alloy. B. show the elastic, plastic and total strain on the diagram stress (Mpa)The data below are for a thin steel wire suitable for use as a guitar string. Ultimate tensile stress: 1.8 x 109 Pa Young Modulus: 2.2 x 1011 Pa Cross-sectional area: 2.0 x 10-7 m2 In a tensile test, a specimen of the wire, of original length 1.5 m, is stretched until it breaks. Assuming the wire obeys Hooke’s law throughout, calculate the extension of the specimen immediately before breaking.
- Following is the Tensile stress-strain data for several hypothetical metals to be used. Answer the following questions referring to table 1.1. Table 1.1: Material Property Data Material Tensile Strength Fracture Strength Strain at Strength (MPa) (MPa) 340 265 550 505 112 150 Fracture before yielding A B C D 0.23 0.15 0.40 a. Which will experience the greatest percent reduction in area? Why? b. Which is the strongest? Why? c. Which is the stiffest? Why? Elastic Modulus (GPa) 210 310 180 400The figure below shows the tensile engineering stress-strain behavior for a steel alloy. (a) What is the modulus of elasticity? (b) What is the yield strength at a strain offset of 0.002? (c) What is the tensile strength? Stress (MPa) 600 500 400 300 200 100 T I 0.00 Stress (MPa) 0.04 500 400 300 200 100 0.000 0.08 0.002 Strain 0.004 Strain 0.12 I 0.006 0.16 0.20 In the previous problem, A load of 85,000 N (19,100 lbf) is applied to a cylindrical specimen of the steel alloy that has a cross-sectional diameter of 15 mm (0.59 in.). (a) Will the specimen experience elastic and/or plastic deformation? Why? (b) If the original specimen length is 250 mm (10 in.), how much will it increase in length when this load is applied?A hypothetical metal has an elastic behavior that follows Hook's law (o = Eɛ) and a plastic behavior that is best described by the following expression: a = -130,023ɛ² + 17,763ɛ + 660.26, where o is in MPa. Furthermore, plastic deformation occurs between strain values 0.0040 and 0.1150, beyond which fracture occurs. Determine the following: a. Modulus of elasticity (GPa) b. Yield strength at strain offset of 0.002 (MPa) Ultimate tensile strength (MPa) C. d. Brinell Hardness e. Resilience (J/m³) f. Ductility (%EI) g. Toughness (T/m³) h. True stress at fracture (MPa)