Fatigue at elevated temperatures

6.11.5 Fatigue at elevated temperatures

At ambient temperature the fatigue process involves intracrystalline slip and surface initiation of cracks, followed by transcrystalline propagation. When fatigued at elevated temperatures ˜>0.5 T m , pure metals and solid solutions show the formation of discrete cavities on grain boundaries, which grow, link up and finally produce failure. It is probable that vacancies produced by intracrystalline slip give rise to a supersaturation which causes the vacancies to condense on those grain boundaries that are under a high shear stress where the cavities can be nucleated by a sliding or ratchet mechanism. It is considered unlikely that grain boundary sliding contributes to cavity growth, increasing the grain size decreases the cavity growth because of the change in boundary area. Magnox (Mg) and alloys used in nuclear reactors up to 0.75T m readily form cavities, but the high-temperature nickel- base alloys do not show intergranular cavity formation during fatigue at temperatures within their normal service range, because intracrystalline slip is inhibited by γ ′ precipitates. Above about 0.7T m , however, the γ ′ precipitates coarsen or dissolve and fatigue then produce cavities and eventually cavity failure.

Problems

6.1 (a) In the diagram the dislocation line is taken to point into the paper. Mark on the diagram the Burgers vector. Under the action of the shear stress shown, which way would the dislocation move?

382 Physical Metallurgy and Advanced Materials (b) If u = [1 1 ¯2], b = 1/2[¯1 1 0] and n = (1 1 1), and the shear stress shown is replaced by

a uniaxial compressive stress σ along [2 0 1], deduce in which direction the dislocation would move. What would be the magnitude of the resolved shear stress on the dislocation?

6.2 A single crystal of aluminum is pulled along [1 1 0]. Which slip system or slip systems operate first?

6.3 Estimate the shear stress at the upper yield point and the yield drop (shear stress) that occurs when the mobile dislocation density increases by two orders of magnitude from the initial density of 10 5 cm −2 . (Take the strain rate to be 10 −3 s −1 ,τ o the stress for unit dislocation velocity of 1 cm s −1 to be 2.8

×10 4 N cm −2 , n to be 20 and b, the Burgers vector, to be

2 × 10 −8 cm.)

6.4 The strengthening of a polycrystalline metal is provided by grain refinement and dispersion of particles. The tensile yield stress of the metal is 400 MPa when the grain size is 0.32 mm and 300 MPa when d = 1 mm. Calculate the average distance between the particles. Assume the shear modulus of the metal μ = 80 GPa and b = 0.25 nm.

6.5 A steel with a grain size of 25 µm has a yield stress of 200 MPa and with a grain size of 9 µm

a yield stress of 300 MPa. A dispersion of non-deformable particles is required to raise the strength to 500 MPa in a steel with grain size 100 µm. What would be the required dispersion spacing? (Assume the shear modulus µ = 80 GPa and the Burgers vector b = 0.2 nm.)

6.6 The deformation mechanism map given in the figure below shows three fields of creep for each of which the creep rate ˙ε (s −1 ) is represented by an expression of the form

n exp( The constant A is 1.5

5 / d 2 ˙ε = Aσ −Q/RT ).

and 10 −9 / d 3 for dislocation creep, Herring– Nabarro creep and Coble creep respectively (d = grain size in m), while the stress exponent n is 5, 1 and 1 and the activation energy Q (kJ mol −1 ) 550, 550 and 400. The stress σ is in MPa. Assuming that the grain size of the material is 1 mm and given the gas constant

R = 8.3 J mol −1 K −1 : (i) Label the three creep fields

(ii) Calculate the stress level σ in MPa of the boundary AB (iii) Calculate the temperature (K) of the boundary AC.

Mechanical properties I 383

Stress (

C Temperature T

6.7 During the strain ageing of a mild steel specimen, the yield point returned after 1302, 420,

C respectively. Determine the activation energy for the diffusion of carbon in α-iron.

90 and 27 seconds when aged at 50, 65, 85 and 100 ◦

6.8 In a high-temperature application an alloy is observed to creep at an acceptable steady-state rate under a stress of 70 MPa at a temperature of 1250 K. If metallurgical improvements would allow the alloy to operate at the same creep rate but at a higher stress level of 77 MPa, estimate the new temperature at which the alloy would operate under the original stress conditions. (Take stress exponent n to be 5, and activation energy for creep Q to be 200 kJ mol −1 .)

= 280 MPa after

10 5 cycles, and for a range 200 MPa after 10 7 cycles. Using Basquin’s law, estimate the life of the component subjected to a stress range of 150 MPa.

Further reading

Argon, A. (1969). The Physics of Strength and Plasticity. MIT Press, Cambridge, MA. Cottrell, A. H. (1964). Mechanical Properties of Matter. John Wiley, Chichester. Cottrell, A. H. (1964). The Theory of Crystal Dislocations. Blackie, Glasgow. Dislocations and Properties of Real Metals (1984). Conf. Metals Society. Evans, R. W. and Wilshire, B. (1993). Introduction to Creep. Institute of Materials, London. Freidel, J. (1964). Dislocations. Pergamon Press, London. Hirsch, P. B. (ed.) (1975). The Physics of Metals. 2. Defects. Cambridge University Press, Cambridge. Hirth, J. P. and Lothe, J. (1984). Theory of Dislocations. McGraw-Hill, New York.

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Chapter 7

Mechanical properties II – Strengthening and toughening