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Improvement of an Exponential Cohesive Zone Model for Fatigue Analysis

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Abstract

Cohesive zone model is an important tool for fatigue analysis, especially for fatigue crack growth along with an interface. A pioneering model is the one of Roe and Siegmund (Eng Fract Mech 70:209–232, 2003), in which the damage accumulation is calculated using an irreversible exponential cohesive law. However, it is found in our recent research that the constant unloading and reloading slope in Roe’s damage evolution law could cause a discontinuity in the traction–separation curve when the mixed mode ratio changes. This limits its application to single mode cyclic loading or scenarios where the mixed mode ratio is constant. In this paper, the cause of such discontinuity is analyzed, and a robust cyclic loading formulation is proposed, which will help the exponential cohesive law remain continuous under arbitrary mixed mode cyclic loading. Moreover, it is found in this paper that by adding a scale factor to the Roe’s damage law, the fatigue failure time can be approximated with less computational cost. The relationship between fatigue failure time and the scale factor is shown to be inversely proportional.

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Abbreviations

β :

Mixed mode ratio

C :

The scale factor in proposed modified damage law

C f :

Endurance limit parameter in Roe’s damage law

d n, d t :

Damage factor in the normal and tangential directions

D :

Fatigue damage

\(\dot{D}_{c}\) :

Fatigue damage accumulation rate

δ 0 :

Mixed mode separation threshold

δ n, δ t :

The normal and tangential separations that correspond to the maximum traction

δ Σ :

Normalization parameter for separation deformation rate

Δ:

Mixed mode separation

\({\dot{\Delta }}\) :

Separation deformation rate

Δmax :

Maximum mixed mode separation in a loading cycle

Δn, Δt :

Normal and tangential separations in exponential cohesive law

Δn0, Δt0 :

Normal and tangential separations on the maximum separation envelope

Δn,max, Δt,max :

Maximum separation in each loading cycle in the normal and tangential directions

K n, K t :

The initial slope of exponential cohesive law in the normal and tangential directions

N c :

Number of loading cycles to fatigue failure with a scale factor C

N 0 :

Number of loading cycles to fatigue failure without a scale factor

ϕ :

Energy release rate

ϕ n, ϕ t :

Mode I and mode II critical energy release rate

r :

Load ratio

σ max,0 :

Normalization parameter for resultant traction

σ min, σ max :

Minimum and maximum stress in cyclic loading

σ mean :

Mean stress in cyclic loading

T, S :

Normal and tangential cohesive strength

T n, T t :

Normal and tangential traction in cohesive law

T n0, T t0 :

Normal and tangential traction on the maximum separation envelope

\(\bar{T}\) :

Resultant traction

T c :

Fatigue failure time with a scale factor C

T 0 :

Fatigue failure time without a scale factor

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Authors and Affiliations

  1. Department of Civil Engineering, University of Cincinnati, Cincinnati, OH, 45220, USA

    Wenlong Zhang

  2. Department of Mechanical Engineering, University of Cincinnati, Cincinnati, OH, 45220, USA

    Ala Tabiei

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  1. Wenlong Zhang
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  2. Ala Tabiei
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Correspondence to Ala Tabiei.

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Zhang, W., Tabiei, A. Improvement of an Exponential Cohesive Zone Model for Fatigue Analysis. J Fail. Anal. and Preven. 18, 607–618 (2018). https://doi.org/10.1007/s11668-018-0434-4

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  • DOI: https://doi.org/10.1007/s11668-018-0434-4

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