The effects of out-of-phase biaxial-strain cycling on low-cycle fatigue

1,544

863

A modification to Brown and Miller's critical plane approach is proposed to predict multiaxial fatigue life under both in-phase and out-of-phase loading conditions. The components of this modified parameter consist of the maximum shear strain amplitude and the maximum normal stress on the maximum shear strain amplitude plane. Additional cyclic hardening developed during out-of-phase loading is included in the normal stress term. Also, the mathematical formulation of this new parameter is such that variable amplitude loading can be accommodated. Experimental results from tubular specimens made of 1045 HR steel under in-phase and 90" out-of-phase axial-torsional straining using both sinusoidal and trapezoidal wave forms were correlated within a factor of about two employing this approach. Available Inconel 718 axial-torsional data including mean strain histories were also satisfactorily correlated using the aforementioned parameter. NOMENCLATURE b = fatigue strength exponent c = fatigue ductility exponent E = modulus of elasticity G = modulus of rigidity K:, = cyclic shear strength coefficient n: = cyclic shear strain exponent n = constant Nf = cycles to failure R = strain ratio, minimum strain/maximum strain S = constant a, = crack angles c, , c2, c3 = principal strains t, = Ac /2 = axial strain amplitude tT = total strain ti = fatigue ductility coefficient AZ/2 = effective strain amplitude ya = Ay/2 = shear strain amplitude y,,, = maximum shear strain 1 = biaxial strain ratio, Ay/At v = Poisson's ratio v, = elastic Poisson's ratio vD = plastic Poisson's ratio u, = A u / 2 = axial stress amplitude (ry = yield strength ( u , ) , , ,~~ = maximum value of the largest principal stress u; = alternating normal stress on yma, plane u; = mean (static) normal stress on ymax plane u; = fatigue strength coefficient 4 = phase angle u y = maximum normal stress on yma, plane T~ = AT/^ = shear stress amplitude 149 F F E M S lI/%A

Section: Test Programmentioning

confidence: 99%

A Critical Plane Approach to Multiaxial Fatigue Damage Including Out‐of‐phase Loading

Fatemi

Socie

1988

1,544

863

“…For the total strain proposed by Zamrik and Frismuth 12 εT = √ε21 + ε22 + ε23 , the following relationship for low‐cycle fatigue was obtained by using uniaxial fatigue behaviours 15…”

Section: Predictions Of Low‐cycle Fatigue Lifementioning

confidence: 99%

A critical plane‐strain energy density criterion for multiaxial low‐cycle fatigue life under non‐proportional loading

Chen

Huang

1999

155

A series of multiaxial low‐cycle fatigue experiments was performed on 45 steel under non‐proportional loading. The present evaluations of multiaxial low‐cycle fatigue life were systematically analysed. A combined energy density and critical plane concept is proposed that considers different failure mechanisms for a shear‐type failure and a tensile‐type failure, and from which different damage parameters for the critical plane‐strain energy density are proposed. For tensile‐type failures in material 45 steel and shear‐type failures in material 42CrMo steel, the new damage parameters permit a good prediction for multiaxial low‐cycle fatigue failure under non‐proportional loading. The currently used critical plane models are a special and simple form of the new model.

“…The above equation can be extended to include non-proportional loading. The additional hardening effect is accounted for by adopting the rotation factor F of reference [9] to modify the cylic strain hardening coefficient K ' , (2) …”

Section: Effect Of Non-proportional Straining On Fatigue Endurancementioning

confidence: 99%

A Path‐independent Parameter for Fatigue Under Proportional and Non‐proportional Loading

Wang

Brown

1993

290

156

A path-independent multiaxial fatigue damage criterion is proposed based on critical plane concepts: fatigue crack growth is controlled by the maximum shear strain, and an important secondary effect is due to the normal strain excursion over one reversal of the maximum shear strain. The effect of loading path on fatigue endurance is quantified by the normal strain excursion. Only one multiaxial material constant is required in the model which can be determined from uniaxial test data plus one torsional result. The parameter can be easily integrated with a shear strain-life relationship to predict low cycle fatigue lifetime. Experimental data of four different materials: En1 5R steel, I % Cr-Mo-V steel, 304 stainless steel, and 316 stainless steel at two temperatures were used to verify the criterion. It is shown that the proposed parameter can satisfactorily correlate test results for various proportional and non-proportional straining paths. NOMENCLATURE b. c = fatigue strength and ductility exponents E = Young's modulus F = rotation factor g = cross hardening coefficient factor K ' , n' = cyclic strength coefficient and strain hardening exponent Nf = fatigue lifetime S = normal strain effect coefficient f = effective shear strain yma, = maximum shear strain t e q , ueq = equivalent strain and stress tn = normal strain across maximum shear plane t: = normal strain excursion between turning points of maximum shear strain v,, vpr vCR = elastic, plastic, and effective Poisson's ratios u;, t i = fatigue strength and ductility coefficients ofl, zfl = uniaxial and torsional fatigue limits