Application of stress-based multiaxial fatigue criteria for laserbeam-welded thin aluminium joints under proportional and non-proportional variable amplitude loadings

Bolchoun, A.; Wiebesiek, J.; Kaufmann, Heinz; Sonsino, C. M.

doi:10.1016/j.tafmec.2014.05.009

Cited by 25 publications

(15 citation statements)

References 11 publications

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“…This is the original formulation by Findley and it cannot be applied to variable amplitude loadings directly, since the values τ a and σ max are not clearly defined in those cases. It is proposed to use Rainflow‐counting‐in‐each‐direction procedure in order to obtain the shear stress amplitudes and maximum normal stresses in each plane . This procedure requires to project the trajectory of the shear stress vector in each plane onto a sufficiently fine sampled number of directions in this plane and subsequently to perform the rainflow counting in each of this direction.…”

Section: Fatigue Life Hypothesesmentioning

confidence: 99%

“…Parameters a, b are material parameters, which take fatigue behavior under pure axial stress and pure torsion into account. In the case discussed in this paper (but not in the original formulation) they also take the Poisson's ratio into account . The values

τ_{eq,m}^{2}

and

σ_{eq,m}^{2}

are stress integrals:

{normalτ}_{eq,a}^{2} = \frac{15}{4 π} {140%\int}_{- \frac{normalπ}{2}}^{\frac{π}{2}} {normalτ}_{θ, ψ, a} \cos ψ d θ d ψ, {normalσ}_{eq,a}^{2} = \frac{15}{4 π} {140%\int}_{- \frac{normalπ}{2}}^{\frac{π}{2}} {140%\int}_{0}^{normalπ} {normalσ}_{θ ψ, a} \cos ψ d θ d ψ

with τ θψ,a and σ θψ,a shear and normal stress amplitudes respectively in a plane, whose normal vector is defined by the angles

θ, ψ

.…”

Section: Fatigue Life Hypothesesmentioning

confidence: 99%

“…Effective equivalent stress hypothesis has an intrinsic capability to take this fatigue life reduction into account. Therefore, an integral measure of non‐proportionality is used :

{normalf}_{NP} = 1 - M, M = \underset{ξ \in thinmathspace[0, π thinmathspace)}{normalmax} \frac{1}{2 {normalπ}^{2}} {140%\int}_{- \frac{normalπ}{2}}^{\frac{π}{2}} {140%\int}_{0}^{2 π} {Cor}^{2} thinmathspace({normalσ}_{normalx}, {normalτ}_{x y} thinmathspace) d θ d ψ

where Cor (σ, τ xy ) is the correlation between the two coordinate stresses σ, τ xy in the coordinate system, whose rotation with respect to the reference coordinate system is defined by the angles θ, ψ and ξ. In order to define the correlation Cor (σ, τ xy ) the following notions are required: The mean value or expected value

E thinmathspace(normalf thinmathspace)

of a function

f : Ω \to ℝ

, where

Ω \subset ℝ

is a bounded domain is defined by the integral:

E thinmathspace(normalf thinmathspace) : = \frac{1}{| Ω |} \underset{normalΩ}{140%\int} f thinmathspace(normalt thinmathspace) d t

The variance Var (f )

Var thinmathspace(normalf thinmathspace)

is given by:

\begin{matrix} left \\ Var thinmathspace(normalf thinmathspace) : = E thinmathsp... \end{matrix}

…”

Section: Non‐proportionality Factormentioning

confidence: 99%

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Experimental results and fatigue life evaluation of magnesium laserbeam‐welded joints under proportional and non‐proportional multiaxial fatigue loading with variable amplitudes

Bolchoun

Sonsino

Kaufmann

et al. 2017

Materialwissenschaft Werkst

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Fatigue life of magnesium laserbeam‐welds (AZ31 and AZ61 alloys) was assessed experimentally under variable amplitude loadings. The specimens were subjected to load‐controlled cyclic loadings. The tests were carried out using a Gauss‐distributed amplitude sequence of length LS = 5 · 104 cycles and loading ratio R = –1 under pure axial, pure torsion as well as in‐phase and out‐of‐phase combined loadings. The notch stresses were obtained from a linear‐elastic FE‐model using the reference radius approach with rref = 0.05 mm. The stress‐based hypotheses were applied: Effective equivalent stress hypothesis (EESH), shear stress intensity hypothesis (SIH), Findley, and modified Gough‐Pollard. A non‐proportionality factor is introduced and steps required for computing are presented in order to improve fatigue life assessment under non‐proportional loadings.

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Section: Fatigue Life Hypothesesmentioning

confidence: 99%

τ_{eq,m}^{2}

and

σ_{eq,m}^{2}

are stress integrals:

{normalτ}_{eq,a}^{2} = \frac{15}{4 π} {140%\int}_{- \frac{normalπ}{2}}^{\frac{π}{2}} {normalτ}_{θ, ψ, a} \cos ψ d θ d ψ, {normalσ}_{eq,a}^{2} = \frac{15}{4 π} {140%\int}_{- \frac{normalπ}{2}}^{\frac{π}{2}} {140%\int}_{0}^{normalπ} {normalσ}_{θ ψ, a} \cos ψ d θ d ψ

with τ θψ,a and σ θψ,a shear and normal stress amplitudes respectively in a plane, whose normal vector is defined by the angles

θ, ψ

.…”

Section: Fatigue Life Hypothesesmentioning

confidence: 99%

“…Effective equivalent stress hypothesis has an intrinsic capability to take this fatigue life reduction into account. Therefore, an integral measure of non‐proportionality is used :

{normalf}_{NP} = 1 - M, M = \underset{ξ \in thinmathspace[0, π thinmathspace)}{normalmax} \frac{1}{2 {normalπ}^{2}} {140%\int}_{- \frac{normalπ}{2}}^{\frac{π}{2}} {140%\int}_{0}^{2 π} {Cor}^{2} thinmathspace({normalσ}_{normalx}, {normalτ}_{x y} thinmathspace) d θ d ψ

E thinmathspace(normalf thinmathspace)

of a function

f : Ω \to ℝ

, where

Ω \subset ℝ

is a bounded domain is defined by the integral:

E thinmathspace(normalf thinmathspace) : = \frac{1}{| Ω |} \underset{normalΩ}{140%\int} f thinmathspace(normalt thinmathspace) d t

The variance Var (f )

Var thinmathspace(normalf thinmathspace)

is given by:

\begin{matrix} left \\ Var thinmathspace(normalf thinmathspace) : = E thinmathsp... \end{matrix}

…”

Section: Non‐proportionality Factormentioning

confidence: 99%

See 1 more Smart Citation

Experimental results and fatigue life evaluation of magnesium laserbeam‐welded joints under proportional and non‐proportional multiaxial fatigue loading with variable amplitudes

Bolchoun

Sonsino

Kaufmann

et al. 2017

Materialwissenschaft Werkst

Self Cite

View full text Add to dashboard Cite

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“…In many practical situations we can find structures and mechanical components subjected to multiaxial random loadings [1][2][3][4]. Examples can be found in energy harvest towers, aircrafts or even in car suspensions.…”

Section: Introductionmentioning

confidence: 99%

Fatigue damage assessment under random and variable amplitude multiaxial loading conditions in structural steels

Anes

Caxias

Freitas

et al. 2017

International Journal of Fatigue

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“…In recent literatures of multiaxial fatigue, it is reported that fatigue life evaluated by the Mises stress is overestimated [1][2][3][4][5][6][7][8] and the M magnitude depends on loading path [9][10][11][12][13][14][15][16]. In the multiaxial fatigue under non-proportional loading in which directions of principal stress and strain are changed in a cycle, it has been reported that fatigue lives are reduced accompanying with additional hardening which depends on both loading path and material [4][5][6][7][8][9][10][11][12][13][14][15][16]. In addition, Itoh et al presented a strain parameter for life evaluation under non-proportional loading considering the intensity of non-proportionality and the material dependency [12,14].…”

Section: Introductionmentioning

confidence: 99%

Multiaxial fatigue property of type 316 stainless steel using hollow cylinder specimen under combined pull loading and inner pressure

Morishita¹,

Takada²,

Itoh³

2017

Frattura Ed Integrità Strutturale

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ABSTRACT. Stress controlled multiaxial fatigue test was carried out using a hollow cylinder specimen of type 316 stainless steel. A newly developed fatigue testing machine which can apply push-pull loading and reversed torsion loading and inner pressure to the hollow cylinder specimen was employed. 5 types of cyclic loading paths were employed by combining zero to pull axial and hoop stresses: a Pull (only axial stress), an Inner-pressure (only hoop stress), an Equi-biaxial (equi-biaxial stress by axial and hoop stresses), a Square-shape (trapezoidal waveforms of axial and hoop stresses with 90-degree phase difference) and a L-shape (alternately axial stress and hoop stress) loading paths. Since directions of principal stresses are fixed in all the tests, all of the loading paths are classified into 'proportional loading'. In the Pull, the Inner-pressure and the Equi-biaxial tests, fatigue lives can be correlated on a unique line by a maximum equivalent stress based on von Mises. On the other hand, fatigue lives in the Square-shape and the L-shape tests were reduced comparing with that in the other tests, which was caused by yielding of larger plastic deformation.

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Application of stress-based multiaxial fatigue criteria for laserbeam-welded thin aluminium joints under proportional and non-proportional variable amplitude loadings

Cited by 25 publications

References 11 publications

Experimental results and fatigue life evaluation of magnesium laserbeam‐welded joints under proportional and non‐proportional multiaxial fatigue loading with variable amplitudes

Experimental results and fatigue life evaluation of magnesium laserbeam‐welded joints under proportional and non‐proportional multiaxial fatigue loading with variable amplitudes

Fatigue damage assessment under random and variable amplitude multiaxial loading conditions in structural steels

Multiaxial fatigue property of type 316 stainless steel using hollow cylinder specimen under combined pull loading and inner pressure

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