Yielding Criteria for Ductile Metal MCQ

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• Stress analysis of structural material for the submarine gives the state of stress as shown in the figure. The yield strength of the material is 450 MPa. Using Tresca’s yielding criteria determine whether yielding will occur or not? If not, what is the factor of safety?
  ক

  Yielding will not occur

  খ

  Yielding will occur, and the factor of safety is 1.125

  গ

  Yielding will occur, and the factor of safety is 1.53

  ঘ

  Yielding will occur, and the factor of safety is 1.28
• The value of constant k in Tresca’s yielding criteria in case of pure shear will be equal to ___________ Given that Principle stress being σ1, σ2, σ3 and yield stress in tension and pure shear are equal to σo and τ.
  ক

  k = σo

  খ

  k = σo/2

  গ

  k = σo/3

  ঘ

  k = σo/4
• Tresca or maximum-shear stress criteria assumes that yielding occurs when the maximum shear stress reaches a value of the shear stress in the uniaxial tension test. Assume the principal stress being σ1, σ2, σ3 where σ1 is largest, and σ3 is the smallest principal stresses. Find the value of minimum shear stress to cause yielding, given that yield stress in tension is equal to σo?
  ক

  τ = σo

  খ

  τ = σo/2

  গ

  τ = σo/3

  ঘ

  τ = σo/4
• Physical Meaning of von-mises yielding criteria is that yielding occurs when the _____________ reaches a critical value.
  ক

  distortion energy

  খ

  strain energy

  গ

  potential energy

  ঘ

  kinetic energy
• According to Von-mises yielding occur when J2 Exceeded some constant k2 So, the minimum condition for yielding is J2 = k2 Find the value of k in state of pure shear. Given that yield strength in pure torsion = τ.
  ক

  τ

  খ

  τ/3

  গ

  τ/√3

  ঘ

  τ/2
• Stress analysis of structural material for the submarine gives the state of stress as shown in the figure. The yield strength of the material is 450 MPa. Using Von-mises yielding criteria determine whether yielding will occur or not? If not, what is the factor of safety?
  ক

  Yielding will not occur

  খ

  Yielding will occur, and the factor of safety is 2.5

  গ

  Yielding will occur, and the factor of safety is 1.53

  ঘ

  Yielding will occur, and the factor of safety is 1.28
• The final result for von-Mises theory for the distortion relating the yield stress with stress deviator is: σo = 1/√2 1/2 Where σo yield stress in uniaxial tension.
  ক

  1/2 Where σo yield stress in uniaxial tension. ] True

  খ

  (σ1-σ2)2+(σ2-σ3)2+(σ3-σ1)2

  গ

  (σ1-σ2)2+(σ2-σ3)2+(σ3-σ1)2

  ঘ

  (σ1-σ2)2+(σ2-σ3)2+(σ3-σ1)2
• According to Von-mises, yielding occurs when J2 exceeds some constant k2 So, the minimum condition for yielding is J2=k2 Find the value of k in uniaxial tension. Given that yield strength = σo
  ক

  σo

  খ

  σo/2

  গ

  σo/3

  ঘ

  σo/√3
• Von-mises or Distortion-energy Criteria proposed that yielding will occur when the second invariant of the stress deviator J2 exceeds some critical value. The second invariant of the stress deviator J2 is equal to __________ b) 1/2 c) d) 1/2
  ক

  1/6

  খ

  (σ1 – σ2)2+(σ2 – σ3)2+(σ3 – σ1)2

  গ

  (σ1 – σ2)2+(σ2 – σ3)2+(σ3 – σ1)2

  ঘ

  (σ1 – σ2)2+(σ2 – σ3)2+(σ3 – σ1)2
• The yielding criteria are primarily empirical relations. Pure hydrostatic stress causes the yielding in continuous solid.
  ক

  True

  খ

  False