Scaling of volume energy density function reflecting damage by singularities at macro-, meso- and microscopic level

Sih, G. C.; Tang, Xue-song

doi:10.1016/j.tafmec.2005.01.006

Cited by 59 publications

(18 citation statements)

References 18 publications

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“…In the case of a notch under free‐clamped conditions, for example, a strong singularity is ever present with ν= 0.5 regardless of the micro‐notch opening angle, whereas weak or no singularities are present under the same boundary conditions for ν= 0.3 25 . The effect of the new singularities at microlevels on the volume energy density function has been analysed by the same researchers 27 …”

Section: Introductionmentioning

confidence: 99%

“…25 The effect of the new singularities at microlevels on the volume energy density function has been analysed by the same researchers. 27 With reference to U-and V-shaped notches in mode I, an interesting bridging exists between the strain energy (SE) and J-integral, 28 when the former is referred to the control volume shown in Fig. 2b and c, the latter to the inner (or the outer) path of the same volume.…”

Section: Introductionmentioning

confidence: 99%

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Brittle failures from U‐ and V‐notches in mode I and mixed, I + II, mode: a synthesis based on the strain energy density averaged on finite‐size volumes

Lazzarin

Berto

Calafat

et al. 2009

Fatigue Fract Eng Mat Struct

137

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A B S T R A C T A large bulk of static test results carried out on notched specimens are presented in a unified way by using the mean value of the strain energy density (SED) over a given finite-size volume surrounding the highly stressed regions. In plane problems, when cracks or pointed V-notches are considered, the volume becomes a circle or a circular sector, respectively, with R C being the radius. R C depends on the fracture toughness of the material, the ultimate tensile strength and the Poisson's ratio. When the notch is blunt, the control area assumes a crescent shape and R C is its width as measured along the notch bisector. About 900 experimental data, taken from recent literature, are involved in the local SED-based synthesis. They have been obtained from (a) U-and V-notched specimens made of different materials tested under mode I loading; (b) U-and V-notched specimens made of polymethyl-metacrylate (PMMA) and an acrylic resin, respectively, tested in mixed, I + II, mode; (c) U-notched specimens made of ceramics materials tested under mode I.The local SED values are normalized to the critical SED values (as determined from unnotched specimens) and plotted as a function of the R/R C ratio. A scatter band is obtained whose mean value does not depend on R/R C , whereas the ratio between the upper and the lower limits are found to be about equal to 1.6. The strong variability of the non-dimensional radius R/R C (ranging here from about zero to around 1000) makes stringent the check of the approach based on the mean value of the local SED on a material-dependent control volume.Keywords brittle fracture; critical radius; finite-size volume; notch; strain energy density. N O M E N C L A T U R Ea = notch depth E = Young's elastic modulus E 1 = strain energy on the control volume f ij , g ij = angular functions F(2α) = parameter to evaluate the strain energy density (blunt notches, R = 0) J = Rice's J integral l ch = characteristic length of the material K I , K U R,I , K V R,I = stress-intensity factor and notch stress-intensity factors for U-and V-shaped notches Correspondence: P. Lazzarin.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Brittle failures from U‐ and V‐notches in mode I and mixed, I + II, mode: a synthesis based on the strain energy density averaged on finite‐size volumes

Lazzarin

Berto

Calafat

et al. 2009

Fatigue Fract Eng Mat Struct

137

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“…Their intensities are influenced by the shape of the notch and by the externally applied loads (Tang and Sih, 2005a). As explained above, in three-dimensional pointed notches with free-clamped edges under nominal anti-plane shear loading all the modes are locally present (Tang and Sih, 2005a;Sih and Tang, 2005). The degree of singularity of the stresses related to different loading modes is strongly influenced by the boundary conditions applied on the notch edges.…”

Section: Introductionmentioning

confidence: 97%

Three-dimensional cracked discs under anti-plane loading and effects of the boundary conditions

Berto

Campagnolo

2015

International Journal of Structural Integrity

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Purpose – Accordingly to the recent multi-scale model proposed by Sih and Tang, different orders of stress singularities are related to different material dependent boundary conditions associated with the interaction between the V-notch tip and the material under the remotely applied loading conditions. This induces complex three-dimensional stress and displacement fields in the proximity of the notch tip, which are worthy of investigation. The paper aims to discuss these issues. Design/methodology/approach – Starting from Sih and Tang’s model, in the present contribution the authors propose some analytical expressions for the calculation of the strain energy density (SED) averaged over a control volume embracing the V-notch tip. The expressions vary as a function of the different boundary conditions. Dealing with the specific crack case, the results from the analytical frame are compared with those determined numerically under linear-elastic hypotheses, by applying different constraints to the through-the-thickness crack edges in three-dimensional discs subjected to Mode III loading. Free-free and free-clamped cases are considered. Findings – Due to three-dimensional effects, the application of a nominal Mode III loading condition automatically provokes coupled Modes (I and II). Not only the intensity of the induced modes but also their degree of singularity depend on the applied conditions on the crack flanks. The variability of local SED through the thickness of the disc is analysed by numerical analyses and compared with the theoretical trend. Originality/value – The capability of the SED to capture the combined three-dimensional effects is discussed in detail showing that this parameter is particularly useful when the definition of the stress intensity factors (SIFs) is ambiguous or the direct comparison between SIFs with odd dimensionalities is not possible.

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“…This is the key idea behind the EDZ model. The damage zone was represented by a restraining stress zone (RSZ) in earlier works . The latest developments of energy density approaches also included the multi‐scale fatigue crack growth models .…”

Section: Introductionmentioning

confidence: 99%

Energy density zone model and fatigue life prediction considering microscopic effects

Zhang

Fan

Tang

2016

Fatigue Fract Eng Mat Struct

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An energy density zone (EDZ) model is developed for the prediction of fatigue life. The microscopic effects can be involved in the EDZ model. Three scale transitional functions in the model are utilized to describe the trans‐scale behaviours of fatigue failure from micro‐scale to macro‐scale. Fatigue failure behaviours of a low‐alloy and ultra‐high‐strength steel material (i.e. 40CrNi2Si2MoVA steel) is investigated. Two fatigue parameters in the model are determined from the experimental S–N curves for the smooth cylinder specimens (the stress concentration factor, SCF, Kt = 1). Then, fatigue lives of notched specimens with SCFs Kt = 2 and Kt = 3 are predicted respectively by the proposed model. The predicted S–N curves are satisfactory in comparison with the experimental results. Scatter of the fatigue test data can be depicted when the microscopic effects are considered. Influences of microscopic effects on the fatigue behaviours are explored by means of numerical simulations.

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Scaling of volume energy density function reflecting damage by singularities at macro-, meso- and microscopic level

Cited by 59 publications

References 18 publications

Brittle failures from U‐ and V‐notches in mode I and mixed, I + II, mode: a synthesis based on the strain energy density averaged on finite‐size volumes

Brittle failures from U‐ and V‐notches in mode I and mixed, I + II, mode: a synthesis based on the strain energy density averaged on finite‐size volumes

Three-dimensional cracked discs under anti-plane loading and effects of the boundary conditions

Energy density zone model and fatigue life prediction considering microscopic effects

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