1. FATIGUE Fatigue of Materials (Cambridge Solid State Science Series) S. Suresh Cambridge University Press, Cambridge (1998) MATERIALS SCIENCE &ENGINEERING Anandh Subramaniam & Kantesh Balani Materials Science and Engineering (MSE) Indian Institute of Technology, Kanpur- 208016 Email: anandh@iitk.ac.in, URL: home.iitk.ac.in/~anandh AN INTRODUCTORY E-BOOK Part of http://home.iitk.ac.in/~anandh/E-book.htm A Learner’s Guide

2.  It is observed that materials subjected to repetitive or fluctuating load (stress) fail at a stress much lower than that required to cause fracture in a single application of a load.  It is estimated that fatigue accounts for ~90% of all service failures due to mechanical causes.  The insidious part of the phenomenon of fatigue failure is that it occurs without any obvious warning.  The surface which has undergone fatigue fracture appears brittle without gross deformation at fracture (in the macroscale).  On a macroscopic scale the fracture surface is usually normal to the direction of the principal tensile stress.  Fatigue failure is usually initiated at a site of stress concentration (E.g. a notch in the specimen or an acicular inclusion).  Three factors play an important role in fatigue failure: (i) value of tensile stress (maximum), (ii) magnitude of variation in stress, (iii) number of cycles. Salient Features Factors necessary to cause fatigue failure Large variation/fluctuation in stress Sufficiently high maximum tensile stress Sufficiently large number of stress cycles

4.  Stress concentration  Corrosion  Temperature  Microstructure  Residual stress  Stress state Factors which play an important role in fatigue

5. Types of stress cycles and parameters characterizing them ← Stress → Cycles → Tensile → ← Compressive aa rr 0 I. Completely reversed cycle of stress

6. II. Purely tensile cycles Cycles → mm rr  max  min Tensile stress → 0

7. III. Random stress cycles Tensile → ← Compressive ← Stress → Cycles → 0

8. S-N Curve  Engineering fatigue data is usually plotted as a S-N curve [S: stress; N: number of cycles to failure (usually fracture), plotted as log(N)]  The stress plotted :  a,  max,  min  Stress values plotted are nominal values (no account for stress concentrations)  Each plot is for a constant  m, R or A  Most fatigue experiments are with  m = 0 (rotating beam tests)  S-N curves deal with fatigue failure at a large number of cycles (> 10 5 )  Stress <  y but microscopic plasticity occurs  Stress   life   For low cycle fatigue (N < 10 4 or 10 5 cycles) tests are conducted in controlled cycles of elastic + plastic strain (instead of stress control)

9. Number of cycles to failure (N) → Bending stress (MPa) → 100 200 0 300 400 10 5 10 6 10 7 10 8 Mild steel Aluminium alloy Fatigue limit Fatigue limit = Endurance limit S-N Curve  Steel, Ti show fatigue limit  Al, Mg, Cu show no fatigue limit No fatigue limit  fatigue strength is specified for and arbitary number of cycles (~ 10 8 cycles)

10. S-N Curve: Basquin equation  S-N curve in the high cycle region is described by the Basquin equation:  a is the stress amplitude, p & C emperical constants  S-N curve is determined using 8-12 specimens  Starting with a stress of two-thirds of the static tensile strength of the material the stress is lowered till specimens do not fail in about 10 7 cycles  Usually there is considerable scatter in the results

11. Strain controlled cyclic loading