The manufacturer of a product that is subjected to repetitive cycles has specified that the product should be removed from service when any crack reaches 15% of the critical crack length required to cause fracture. Consider a crack that is initially 0.02 mm long in a material with a fracture toughness of 55 MPaVm. The product is continuously cycled between compres- sive and tensile stresses of 300 MPa at a constant frequency. Assume external cracks for whichƒ= 1.12. The materials constants for these units are n- 3.4 and C- 2x 10-1. (a) What is the critical crack length required to cause fracture? (b) How many cycles will cause product failure? (c) If the product is removed from service as specified by the manufacturer, how much of the useful life of the product remains?

A 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.

A brass specimen of the circular cross-section is fractured at 151 kN force and the final length of the specimen at fracture is 48 mm. The fracture strength of the specimen is found to be 72 kN/mm?. The percentage of elongation of the specimen is 44 %. Determine the following (i) Diameter of the specimen, ii) Initial length of the specimen, iii) Stress under an elastic load of 15 kN, iv) Young's Modulus if the elongation is 1.5 mm at 15 kN (v) Final diameter if the percentage of reduction in area is 21 %. ( Initial Cross-sectional Area (in mm?) The Diameter of the Specimen (in mm) Initial Length of the Specimen (in mm) Stress under the elastic load (in N/mm?) Young's Modulus of the Specimen (in N/mm2) Final Area of the Specimen at Fracture (in mm) Final Diameter of the Specimen after Fracture (in mm)

The principal stresses at a point are 20 (tensile) and o (compressive), and the stress at elastic limit for the material in simple tension is 210 N/ mm². According to maximum shear strain theory, the value of oat failure is (a) 70 N/mm² (c) 140 N/mm² (b) 105 N/mm² (d) 210 N/mm²

compare the effect of presence of a notch on ductile and brittle materials in terms of fracture behaviour

State the difference between cleavage and fracture of minerals, using quartz and mica as examples.

(b) An aluminium plate (100 mm width x 300 mm height x 4 mm thick) with a centre-crack is subjected to a mode-l service load of 40 kN. Assume that the fracture toughness of the material is 24 MPa Vm and Y-1.0. (ii) What is the safety factor on crack length? Assume that the yield strength of aluminium is 425 MPa.

Is the fracture in the picture below brittle or ductile? Where is the location of the initiation of the fracture and why?

2. The Goodman diagram relates oa and om for fatigue failure after a specific number of cycles Nf, where da is the cyclic stress amplitude, and om the mean stress. For a steel specimen it is found that oa oa (0). [1- (om/OTS)] where Ors is the metal's tensile stress (375MPa), and oa (0)~0.450TS is the 107 cycle fatigue limit at zero mean stress. Assuming the specimen is cycled repeatedly between 0 stress and a peak stress, what is the maximum peak stress if failure in < 107 cycles is to be avoided? Ans: 233 MPa

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