Find the strain proportions (ɛ1:E2:E3) that existed in a forming process where O3= 0. Also specify two conditions that can be used the stresses are ơ1 02=01/3 , to describe the deformation process.
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- A strain rosette (see figure) mounted on the surface of an automobile frame gives the following readings: gage A,310 × 10-6:gage B,180 × l0-6; and gage C. -160 × 10-6. Determine the principal strains and maximum shear strains, and show them on sketches of properly oriented elements.Tensile test specimens are extracted from the "X" and "y" directions of a rolled sheet of metal. "x" is the rolling direction, "y" is transverse to the rolling direction, and "z" is in the thickness direction. Both specimens were pulled to a longitudinal strain = 0.15 strain. For the sample in the x-direction, the width strain was measured to be ew= -0.0923 at that instant. For the sample in the y-direction, the width strain was measured to be gw=-0.1000 at that instant. The yield strength of the x-direction specimen was 50 kpsi and the yield strength of the y-direction specimen was 52 kpsi. Determine the strain ratio for the x direction tensile test specimen. Determine the strain ratio for the y-direction tensile test specimen. Determine the expected yield strength in the z-direction. Give your answer in units of kpsi (just the number). If the sheet is plastically deformed in equal biaxial tension (a, = 0, to the point where & = 0.15, calculate the strain, 6, that would be expected.Example: Convert the change in length data in Table 3-2 to engineering stress and strain and plot a stress-strain curve Homework- help Table 3-2 The results of a tensile test of a 0.505 in. diameter aluminum alloy test bar, initial length (1o) = 2 in. Calculated LTO Load (Ib) Change in Length (in.) Stress (psi) Strain (in./in.) 0.000 1000 0.001 0.0005 4,993 14,978 24,963 34,948 37,445 39,442 39,941 39,691 37,944 3000 0.003 0.0015 5000 0.005 0.0025 7000 0.007 0.0035 7500 0.030 0.0150 7900 0.080 0.0400 8000 (maximum load) 0.120 0.0600 7950 0.160 0.0800 7600 (fracture) 0.205 0.1025
- Question-1: The strain rosette shown in the figure was used to obtain normal strain data at a point on the free surface of a machine part. (a) Determine the strain components &, S, and %, at the point. (b) Determine the principal strains and the maximum in-plane shear strain at the point. (c) Draw a sketch showing the angle 6, the principal strain deformations, and the maximum in-plane shear strain distortions. (d) Determine the magnitude of the absolute maximum shear strain. 45 45 &- 50 με, 8--730 με , ε375 με, ν-0.301. We can visualize the factor of safety for an arbitrary stress using a surface in principal stress space. For a ductile material that yields according to a von Mises criterion with a yield stress σy, sketch the von Mises surface in σ₁ - 02 space and sketch the stress surface that corresponds to a factor of safety FoS = 2. For a brittle material that yields according to a max normal (Rankine) criterion with a tensile strength Gyt and a compressive strength σvc = 20yt, sketch the yield surface and the surface that corresponds to a factor of safety FoS = 2.Question: The stress components at point O of a part made of steel material (E = 210 GPa and v= 0.3) are given below. 25 40 - 20 40 30 35| MPа - 20 35 -10 a) Calculate the strain components (Exx, Eyy, Ezz, Yxy, Yxz and Yyz). b) Calculate the principal strain components (E,, E2, and E3) and the maximum shear stress (max). c) Draw the 3-D Mohr circle for the strain components.
- ? (sigma) = 90 40 0 40 −50 0 0 0 0 MPaa. Plot the shear and normal stresses on a given oblique plane (rotated plane) on a graph (stress vs. angle) and show the max. shear plane and the principal planes. (like in the image, using excel) b.If the steel sample has a Young’s modulus of 193 GPa, compute the dimensional changes of the plate under the above loading condition. Shear moduli is 70Gpa.Problem F2 stress (ksi) 130 120 110 100 90 80 70 60 50 40 30 20 10 0 0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 strain (in/in) Above you will find the experimental stress-strain diagram of 1045 steel. Calculate the permanent set if a cylindrical specimen with a diameter of 2 in is loaded to the ultimate stress and then unloaded. Provide your answer in units of in/in with 3 significant figures after the decimal. The elastic modulus of 1045 steel is 29,000 ksi.The state of plane stress shown occurs at a critical point of a metal machine component. As a result of several tensile tests, it has been found that the tensile yield strength is Fy for the grade of metal used. Determine the ratio of OT/ OH shown in the figure, using the maximum-shearing-stress criterion (Tresca Hexagon). (Using Mohr circle method to calculate principle and average stresses) OX TXy Mpa Mpa Mpa MPa ob σy тху 90 -60 45 310 dy OX x Sx=Sx Sy=sy txy=txy Fy=Yield Strength Answer
- Electrical strain gauges were applied to a notched specimen to determine the stresses in the notch. The results were ex = 0.0019 and ey = -0.00072. Find ox and ay if the material is carbon steel.diagram and determine approximately the modulus of elasticity, the yield stress, the ultimate stress, and the fracture 2.00 in. The data is listed in the table. Plot the stress-strain 8-1. A tension test was performed on a steel specimen n original diameter of 0.503 in. and gage length of PROBLEMS *84. origi the f having an for t and stress. Use a scale of 1 in. Dodraw the elastic region, using the same stress scale but a 20 ksi and 1 in. = 0.05 in./in. strain scale of 1 in.= 0.001 in./in. Load (kip) Elongation (in.) 0. 0. 0.0005 0.0015 1.50 4.60 8.00 11.00 0.0025 0.0035 0.0050 11.80 11.80 0.0080 0.0200 12.00 16.60 0.0400 0.1000 0.2800 20.00 21.50 19.50 18.50 0.4000 0.4600 Prob. 8-1Stress Strain Diagram The Data shown in the table have been obtained from a tensile test conducted on a high-strength steel. The test specimen had a diameter of 0.505 inch and a gage length of 2.00 inch. Using software. plot the Stress-Strain Diagram for this steel and determine its: A= TTdT(050s A %3D 1. Proportional Limit, 2. Modulus of Elasticity, 3. Yield Strength (SY) at 0.2% Offset, 4. Ultimate Strength (Su), 5. Percent Elongation in 2.00 inch, 6. Percent Reduction in Area, 7. Present the results (for Steps 1-6) in a highly organized table. e Altac ie sheet (as problelle 4 A = 0.2.002 BEOINNING of the effort Elongation (in) Elongation (In) Load Load #: #3 (Ib) (Ib) 1 0.0170 15 12,300 0.0004 1,500 16 12,200 0.0200 0.0010 3. 3,100 17 12,000 0.0275 0.0016 4,700 18 13,000 0.0335 5. 6,300 0.0022 19 15,000 0.0400 0.0026 6. 8,000 20 16,200 0.055 0.0032 9,500 21 17,500 0.0680 0.0035 8. 11,000 22 18,800 0.1080 0.0041 11,800 23 19,600 0.1515 0.0051 24 20,100 0.2010 10 12,300 0.0071 25…