1. Consider the following stress-strain responses of metallic materials:

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1 TECNOLOGIA MECÂNICA Mestrado em Engenharia de Materiais January 3, 2015 Number: Name: 1. Consider the following stress-strain responses of metallic materials: Y Load Unload Y E Load E Unload Y (1) (2) (3) 1.1. Choose the correct legend for each figure. a) 1-Rigid-perfectly plastic, 2-Elasto-plastic, 3- Rigid-plastic b) 1-Rigid-perfectly plastic, 2- Rigid-linear elastic, 3- Rigid-plastic with pre-strain c) 1-Elasto-linear plastic, 2-Elasto-plastic, 3-Rigid-plastic with pre-strain d) 1-Linear elasto-plastic, 2- Elasto-plastic, 3-Rigid-plastic 1.2. Plot the load and unload paths in figure 3 and identify the slope of the unloading path. 1.3 Which is the most appropriate stress-strain equation to model the stress-strain response of the material illustrated in figure 3. n a) K b) c) n Y K K ( 0 ) n d) H Y e) A B exp C

2. A cube made from a metallic material with a yield stress Y is subjected to the following loading: 1 0, 2 0 e 3 1. 2.1 Choose the correct answer for the principal stresses at the onset of plastic deformation.

2 2. A cube made from a metallic material with a yield stress Y is subjected to the following loading: 1 0, 2 0 e Choose the correct answer for the principal stresses at the onset of plastic deformation. a) 1 Y, 0, 3 Y 2 b) Y 1 2, 2 0, 3 Y 2 c) Y 1, 2 0, 3 3 Y 2 2 d) 1 Y, 2 0, 3 Y Choose the correct answer for the increment of plastic strain vector ( d, d, d ) at the onset of plastic deformation. 3 a) d 3 1, 0, d b) d 3 1, 0, d d 1 d d c) 1, 2, d 3 d d) Y, 0, Y 2 2

3 3. Consider the fine blanking process and select the wrong sentence. a) Fine blanking provides excellent tolerance and morphology of the cut surfaces enabling its utilization without the need to perform secondary finishing operations. b) Tools in fine blanking are more complex and expensive than in conventional blanking due to the utilization of blank holders with V-rings and counterpunches (cushions) although clearances between the punches and the dies being similar to those utilized in conventional blanking. c) In fine blanking, the combined action of the V-ring and counterpunch imposes hydrostatic compression states, which will counteract crack formation and allow cutting to take place entirely by plastic deformation, resulting in full smooth and shiny surfaces. d) The work and the maximum cutting force in fine blanking are higher than in conventional blanking. 4. Consider the bottom region of a cylindrical cup during the first stage (stretching) of a deep drawing operation. j 1 B Y A 1-2 B 1-1/2 C A D E 1 FLC 1 2 Y C Y D Y k i 4.1 Identify the strain loading path in the principal strain space. 4.2 Identify the quadrant of the principal stress space where the stresses are located. 4.3 Identify the quadrant of the principal stress space where the stresses of the flange area are located during the second stage of a deep drawing performed without blank holders.

d) Estimate the increase of temperature assuming that 85% of the plastic work is converted into heat. Additional data: 0.180 Stress-strain equation: 154.5 MPa. Density: 2.

4 5. Cold extrusion of an aluminum AA6060-O rod is utilized to reduce its diameter from 50 mm to 45 mm. The overall efficiency of the process is 60%. a) Determine the yield stress of the material after being extruded. b) Estimate the pressure applied on the die at the entry. c) Calculate the extrusion force by means of the ideal work method. d) Estimate the increase of temperature assuming that 85% of the plastic work is converted into heat. Additional data: Stress-strain equation: MPa. Density: 2.7 g/cm 3 Specific heat: 897 J/kgK 6. Consider orthogonal metal cutting of stainless steel. Rake angle: 10º Uncut chip thickness (depth of cut): 0.05 mm Chip Thickness: 0.08 mm Width of the chip: 10 mm Cutting velocity: 1m/s Friction coefficient: 0.5 Specific cutting pressure (specific cutting energy): 3500 MPa a) Estimate the value of the shear plane angle b) Calculate the resultant force c) Calculate the shear stresses in the shear plane. d) Calculate the cutting power e) Calculate the volume rate of material removal.

5 TECNOLOGIA MECÂNICA Mestrado em Engenharia de Materiais January 3, 2015 Number: Name: This A4 sheet is part of your exam. Please deliver it together with the other A4 sheets of your exam. Information: Total duration: 2h 30m Only answers to questions 5 and 6 may be provided in separated A4 sheets. The two formula data sheets available at the internet page of the course can be used. Classifications (negative points apply in some wrong answers): Question Partial classification Answer (Yes/No) Question Partial classification Answer (Yes/No) (-0.5) 5a b (-0.5) 5c (-0.5) 5d (-0.5) 6a (-1.0) 6b (-0.5) 6c (-0.5) 6d (-0.5) 6e 1.0

Fundamental Course in Mechanical Processing of Materials. Exercises

Fundamental Course in Mechanical Processing of Materials Exercises 2017 3.2 Consider a material point subject to a plane stress state represented by the following stress tensor, Determine the principal