Effects of friction and high torque on fatigue crack propagation in Mode ...

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Feb 26, 1982 - Abstract. Turbo-generator and automotive shafts are often subjected to complex histories of high torques. To provide a basis for fatigue lifeĀ ...
Effects of Friction and High Torque on Fatigue Crack Propagation in Mode III H. NAYEB-HASHEMI, F.A. McCLINTOCK, and R. O. RITCHIE Turbo-generator and automotive shafts are often subjected to complex histories of high torques. To provide a basis for fatigue life estimation in such components, a study of fatigue crack propagation in Mode II1 (anti-plane shear) for a mill-annealed AIS14140 steel (RB88, 590 M N / m 2 tensile strength) has been undertaken, using torsionally-loaded, circumferentially-notched cylindrical specimens. As demonstrated previously for higher strength AISI 4340 steel, Mode III cyclic crack growth rates (dc/dN)m can be related to the alternating stress intensity factor AKinfor conditions of small-scale yielding. However, to describe crack propagation behavior over an extended range of crack growth rates (-- 10-6 to 10-2 mm per cycle), where crack growth proceeds under elastic-plastic and full plastic conditions, no correlation between (dc/dN)lll and AKu~ is possible. Accordingly, a new parameter for torsional crack growth, termed the plastic strain intensity l"m, is introduced and is shown to provide a unique description of Mode III crack growth behavior for a wide range of testing conditions, provided a mean load reduces friction, abrasion, and interlocking between mating fracture surfaces. The latter effect is found to be dependent upon the mode of applied loading (i.e., the presence of superimposed axial loads) and the crack length and torque level. Mechanistically, high-torque surfaces were transverse, macroscopically flat, and smeared. Lower torques showed additional axial cracks (longitudinal shear cracking) perpendicular to the main transverse surface. A micro-mechanical model for the main radial Mode III growth, based on the premise that crack advance results from Mode II coalescence of microcracks initiated at inclusions ahead of the main crack front, is extended to high nominal stress levels, and predicts that Mode III fatigue crack propagation rates should be proportional to the range of plastic strain intensity (AFro) if local Mode II growth rates are proportional to the displacements. Such predictions are shown to be in agreement with measured growth rates in AISI 4140 steel from l0 -6 to l0 -2 mm per cycle.

I.

INTRODUCTION

R O T A T I N G equipment, such as turbo-generator rotors utilized for electrical power generator and transmission shafts for automotive use, are often subjected to transient high amplitude torsional oscillations which may severely limit the useful life of the structure through subcritical crack growth of undetected flaws. High strain amplitudes, approaching full-scale yielding of the shaft, can arise following electrical transients from particular line switching events in electric power generation and transmission systems. ~'2'3 At such high torques, fatigue growth occurs in anti-plane shear (Mode III) along transverse and/or longitudinal shear planes. 4'5 However, methodology to predict the Mode III growth of such flaws and hence to estimate the loss in fatigue life due to transient torsional oscillations is currently lacking for variable amplitude (spectrum) loading. There is a distinct lack of engineering data relating the growth rate of Mode III cracks to relevant loading parameters and the various modes of torsional fractures are poorly understood, in contrast to the wealth of information on fatigue crack propagation under Mode I (tensile opening) conditions. In both

H. NAYEB-HASHEMI, Postdoctoral Research Associate, and F.A. McCLINTOCK, Professor, are both with the Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139. R.O. RITCHIE, formerly with Massachusetts Institute of Technology, is Professor, Department of Materials Science and Mineral Engineering, and Materials and Molecular Research Division, Lawrence Berkeley Laboratory, University of California, Berkeley, CA 94720. Manuscript submitted February 26, 1982. METALLURGICALTRANSACTIONS A

cases fundamental, quantitative understanding based on growth mechanisms is not available. The objective of the present paper is to provide an experimental and theoretical basis for characterizing Mode III fatigue crack growth under both small-scale yielding and elastic-plastic conditions in a low strength, low alloy steel. The approach combines continuum fracture mechanics and preliminary mechanistic modeling to serve as a framework for the development of defect-tolerant life estimation procedures for components loaded to high torques. II.

BACKGROUND

Despite the relative scarcity of experimental studies on Mode III crack growth, several analytical models have been developed over the years. The problem of fully plastic fatigue of longitudinal shear cracks was first analyzed by McClintock, 6 and extended by Hult 7 for elastic-plastic conditions. A damage-accumulation model was later proposed by Kayan s where the crack was considered to propagate at a rate consistent with the damage, or fraction of life expended, remaining constant at unity at a structural distance p ahead of the crack. Since crack advance was modeled as hole growth from inclusions or shear localization on specific slip planes, the value of p could be related to the mean inclusion spacing or representative slip band length. Later studies 9 generalized these models for elastic-plastic conditions to predict growth rates as a function of plastic zone size, and qualitative agreement was found with experimental measurements on longitudinal cracks in torsionallyloaded rectangular b a r s . 6-9 More recently, failure criteria

ISSN 0360-2133/82/1211-2197500.75/0 9 1982 AMERICAN SOCIETY FOR METALS AND THE METALLURGICALSOCIETY OF A/ME

VOLUME 13A, DECEMBER 1982--2197

based on a critical crack tip displacement (CTD) have been incorporated, both for constant amplitude4 and variable amplitude5 loading, where the crack is considered to grow in proportion to some fraction of the CTD on each reversal. Subsequent to the early measurements described above,6-9 growth rate data and microstructural observations on Mode III crack growth have been largely unavailable. Very recently, however, studies on En 161~ and AISI 43404'11 steels have indicated that rates of Mode III crack growth (dc/dN)m can be power-law related to AKin, the Mode III stress intensity range, for nominal conditions of small-scale yielding. Further, it was found4 that Mode III crack velocities (dc/dN)m, for concentrically-radial cracks in torsionally-loaded cylinders, were only a small fraction (--0.0005 to 0.002) of the cyclic crack tip displacement (ACTDIn) per cycle, in contrast to Mode I behavior where the fraction is much larger (0.01 to 0.1). Micro-mechanical modeling, 4 based on early observations 12 that Mode III cracking can occur by a Mode II shear coalescence of microcracks initiated at inclusions ahead of the crack front, verified this small dependence on ACTDIn. To date, supporting growth rate data have been expressed in terms of linear elastic parameters, such as AKin.*'l~ This poses a severe limitation to the description of Mode III behavior for which the plastic zone sizes are large. Consequently, the present work on low strength steel was undertaken to extend the fracture mechanics characterization of torsional crack growth rates to elastic-plastic conditions by proposing an alternative crack growth parameter.

III.

PLASTIC STRAIN INTENSITY CONCEPT

Since at low stress intensities (i.e., growth rates below - 1 0 -6 mm per cycle) there is a transition from Mode III to Mode I cracking (see also Reference 4), extensive plasticity is apparently necessary to promote Mode III growth. Thus, to provide a unique description of crack growth in anti-plane shear, crack growth parameters other than the elastic stress intensity factor AKIn must be used. Computational and experimental difficulties with the crack tip displacement (CTD)In and J-integral concepts as applied to the large-scale yielding of circumferentially-notched cylindrical specimens led to the choice of a new parameter, termed the plastic strain intensity Fin, described in detail below. Analytical solutions for the strain distribution in a circumferentially-cracked solid cylinder of an elastic-rigid plastic material subjected to a torque M indicate that the distribution of plastic strain in the plane of the crack is given by Reference 13:

k(~)E(rzrP~ Y = -G \r~ - r~

[11

where y is the plastic shear strain, k the shear yield stress, G the shear modulus, and r, rN, and rp are radii defined ahead of the crack tip in Figure 1. Although the plastic strain is infinite at the crack tip (r = rN), the parameter y(rN - r) is clearly finite and further defines the intensity of plastic shear strain in the crack plane, namely

FIn = y(rN - r) = k (1 - rp/rN) rN G

at r ---->rN 2198--VOLUME 13A, DECEMBER 1982

(r~/r~) 2

[21

T

!

,o _

I

~____~u

~ Plastic

7--1 rp ,

- -

Region

C~---

.7

Fig. 1--Dimensions for plastic zone and respective radii in circumferentiallynotchedspecimen. Computation of Fin involves determining an analytical expression for rp/rN. Limiting cases for the ratio of applied torque to limit torque for M / M L ~ 0 (elastic) and M/ML ~ 1 (fully plastic) are given by Reference 13:

16 ( M-M-~2( r~ - 1) 9 \ML] \rN rplrN = 1 -- 1 + 649\rN(ro_ 1) '

M as --ML~ 0

[3]

and

(rp/ru) 3 = 4(1

-

M/ML)

M as-- ~ 1 ML

'

[4]

where r0 is the external radius of the testpiece. Interpolation between these limits using the analytical results in Reference 13 leads to the following approximate expression for rp/rN for 0 --< M/ML -< 1, namely

rplrs = 1 -- q(M /ML) 2 - (M/ML)4 [1 - q - 1.5873(1 - M/ML) 1/3] - 3.17[(MIML) 5 - (MIML) 6] where

[5]

16(r 't q=

9

64(ro_ 1+ 9\rN

[6] 1)

Hence, within the boundary conditions of the circumferentially-notched cylindrical test-piece, the parameter Fm defined from Eqs. [1] and [6] characterizes the intensity of plastic shear strain in the crack plane ahead of the crack tip. We thus propose this parameter, termed the plastic strain intensity, as a governing parameter for Mode III fatigue crack propagation in the presence of extensive plasticity (0