Two- and three-dimensional elastic-plastic stress analysis for a double edge notched tension specimen

Fatigue macrocrack initiation is considered to be a two‐parameter process. It is governed by the local or strain amplitude, and a certain linear parameter of the material. Corresponding parameters have been proposed, i.e. the local stress range Δσ*y and a characteristic distance d *, the prefracture zone size. The formation of this zone is conditioned by a decrease in yield strength within the material’s surface layers, microstructure, loading amplitude, cyclic strain hardening and environment. The value of d * is estimated experimentally by several methods and is assumed to be a certain material constant, independent of both notch and specimen geometry. At the prefracture zone boundary, a major barrier exists that retards the growth of a physically small fatigue crack. The moment when the physically small crack overcomes the prefracture zone boundary is assumed to be a quantitative criterion, ai = d *, for the micro‐ to macrocrack transition. The proposed relationships, Δσ*y versus Ni , and d * versus Ni , can be used as a basis for the establishment of the materials resistance to macrocrack initiation.

Section: A Phenomenological Model Of Fatigue Macrocrack Initiationmentioning

confidence: 67%

A phenomenological model of fatigue macrocrack initiation near stress concentrators

Ostash

Panasyuk

Kostyk

1999

“…Part of the difference is obviously due to the plane stress calculation model, in which the constraining effect between hard and soft phases is lower than that in a three-dimensional stress state of actual materials. Thus, the calculated stress-strain curve is somewhat softer than the experimental curve [17,181. Part of this difference could be also due to the input of the martensite behavior data, which was obtained from steel M, the latter being softer than that in dual phase steel.…”

Section: Resultsmentioning

confidence: 83%

Low‐cycle Fatigue Investigations and Numerical Simulations on Dual Phase Steel With Different Microstructures

Jiangbuo

Wang

et al. 1990

Fully reversed low cycle fatigue tests were carried out on 7 mm diameter cylindrical specimens of a dual phase steel treated to give five different microstructures, namely F-ferrite ( + little carbide particles), CF-ontinuous ferrite + 8.2% martensite, FM-49.1 YO ferrite + 50.9% martensite mixed structure, CM-continuous martensite + 22.4% ferrite and M-I00% martensite. A finite element program was developed based on Eisenberg's cyclic plasticity theory and the low cycle stress--strain response of the steels with duplex phase microstructures was calculated from the low cyclic curves of the single ferrite (steel F) and martensite (steel M) phase. The experimental results show that fatigue performance of dual phase steel improves as martensite content is increased up to about 50%, thereafter it obviously deteriorates. During cyclic loading, the calculated plastic strain accumulated in ferrite is higher than that in martensite. Inhomogeneity of the plastic strain accumulation in steel C F is more pronounced than that in steel CM. In steel FM a relatively uniform strain distribution was found. Controlling the size of particle phase can result in an optimum strain distribution. Thus, the plastic deformation capability of the constituent phases can be enhanced leading to fatigue performance improvement. Crack initiation occurs easily at the ferrite/martensite interface with a coarse particle phase size, regardless of phase continuity. In steel CF, a crack initiates at the interface perpendicular to the stress axis and propagates in the ferrite matrix by deflecting around coarse martensite particles or by cutting fine martensite particles. In steel CM, a crack initiates at the interface along the stress axis and propagates in the martensite matrix through ferrite particles.

“…On the other hand, Twickler et aZ. [2] interpreted the oscillations of their numerical results as a result of an unaccepted element aspect ratio. It is known that the size and the aspect ratio of the element play a vital role in the accuracy of the solution.…”

Section: Analysis and Correlationmentioning

confidence: 99%

Front Development of a Long Fatigue Crack During Its Growth

Hammouda

Seleem

Sallam

et al. 1997

A 3-D elastic-plastic finite element analysis has been developed to simulate the deformation development along the front of a long mode I single edge crack in plates subjected to either monotonic or cyclic loading. Idealisations having both equal and unequal layers through the thickness of the plate were involved. Plane stress and plane strain 2-D finite element analyses were also performed and compared with the present 3-D solutions. The development of the monotonic and cyclic crack tip plastically deformed zones and opening displacements were traced and correlated to accommodate the effect of the plate thickness and the profile of the crack front. A previously developed crack tip deformation parameter was invoked to predict the effect of the specimen thickness on mode I fatigue crack growth and the associated change of crack front profile. Comparison of such a prediction and the experimental findings of the present work reflected the capability of that parameter in modelling fatigue crack growth through the plate thickness. NOMENCLATURE Symbolsa, b =height and base, respectively of a triangular slit symmetrically made along the main TSSF dl/dN = FCG rate F,, F2 = CTD,,/CTD,, and CTDJCTD,, respectively F3 = CTDJCTD,,=layer thickness x, y, z = co-ordinate system Y = geometry factor defined by the mathematical expression of the SIF w, t = plate width, and half plate thickness LY, q, p, y, 3, = fitted parameters 6, A6 = extent of CTOD, and cyclic CTOD A = extent of CTPDZ Ao, gy = stress range and monotonic yield stress, respectively Subscripts c = cyclic cl = closure cs =cyclic value for a stationary crack m = monotonic c2D = cyclic value for two-dimensional plane stress max, min = maximum and minimum ms =monotonic value for a stationary crack m2D = monotonic value given by the two-dimensional plane stress s, ss = along the front of a stationary crack and along the front of a TSSF, respectively s2D =given by the two-dimensional plane stress state for a stationary crack 849 850 M. M. I. HAMMOUDA et al. AbbreviationsCTA, CTD = crack tip advance and crack tip deformation CTC = crack tip closure CTDF, CTOD = crack tip deformation factor, and crack tip opening displacement, respectively CTPDZ = crack tip plastically deformed zone ELI = equal layer idealisation FCG = fatigue crack growth FEA = finite element analysis SIF = stress intensity factor TSSF = through-thickness stationary crack having a straight front ULI = unequal layer idealisation 2-D, 3-D = two-dimensional and three-dimensional