scholarly journals Cohesive fracture with irreversibility: Quasistatic evolution for a model subject to fatigue

2018 ◽  
Vol 28 (07) ◽  
pp. 1371-1412 ◽  
Author(s):  
Vito Crismale ◽  
Giuliano Lazzaroni ◽  
Gianluca Orlando
Keyword(s):  
Crack Surface ◽  
Crack Opening ◽  
Young Measure ◽  
Small Strain ◽  
Weak Formulation ◽  
Cohesive Fracture ◽  
Quasistatic Evolution ◽  
Antiplane Elasticity ◽  
Energy Dissipated ◽  
Model Subject

In this paper we prove the existence of quasistatic evolutions for a cohesive fracture on a prescribed crack surface, in small-strain antiplane elasticity. The main feature of the model is that the density of the energy dissipated in the fracture process depends on the total variation of the amplitude of the jump. Thus, any change in the crack opening entails a loss of energy, until the crack is complete. In particular this implies a fatigue phenomenon, i.e. a complete fracture may be produced by oscillation of small jumps. The first step of the existence proof is the construction of approximate evolutions obtained by solving discrete-time incremental minimum problems. The main difficulty in the passage to the continuous-time limit is that we lack of controls on the variations of the jump of the approximate evolutions. Therefore we resort to a weak formulation where the variation of the jump is replaced by a Young measure. Eventually, after proving the existence in this weak formulation, we improve the result by showing that the Young measure is concentrated on a function and coincides with the variation of the jump of the displacement.

On the determination and application of cod to epoxy-bonded aluminium joints

1979 ◽  
Vol 14 (2) ◽  
pp. 37-42 ◽  
Author(s):  
C L Chow ◽  
C W Woo ◽  
J L Sykes
Keyword(s):  
Crack Opening ◽  
Load Control ◽  
Yield Model ◽  
Cohesive Fracture ◽  
Element Analysis ◽  
Testing Conditions ◽  
Strip Yield Model ◽  
Dimensional Finite Element ◽  
Good Agreement

A method of analysis is presented for the determination of crack-opening-displacements (COD) and their application to aluminium—Araldite joint systems. Use is made of a beam-on-elastic-foundation (BEF) model, which is extended to represent the physical system. It is seen that, in conjunction with this, the Dugdale ‘strip-yield’ model solution may be combined to characterize interfacial or cohesive fracture cases. Fracture toughness values, based on both load and displacement control testing conditions, are examined and show that the equation derived for the load-control model yields greater accuracy. Results of the proposed method are compared with those obtained by a two-dimensional, finite-element analysis and are found to be in good agreement. The validity of the proposed analysis is further verified by experimental observations employing conventional compliance methods for both interfacial and cohesive fracture modes.

scholarly journals Periodic Array of Cracks in a Half-Plane Subjected to Arbitrary Loading

1987 ◽  
Vol 54 (3) ◽  
pp. 642-648 ◽  
Author(s):  
H. F. Nied
Keyword(s):  
Integral Equation ◽  
Half Plane ◽  
Crack Surface ◽  
Mixed Boundary ◽  
Crack Opening ◽  
Periodic Array ◽  
Hypersingular Integral Equation ◽  
Opening Displacement ◽  
Surface Displacements ◽  
Displacement Based

The plane elastic problem for a periodic array of cracks in a half-plane subjected to equal, but otherwise arbitrary normal crack surface tractions is examined. The mixed boundary value problem, which is formulated directly in terms of the crack surface displacements, results in a hypersingular integral equation in which the unknown function is the crack opening displacement. Based on the theory of finite part integrals, a least squares numerical algorithm is employed to efficiently solve the singular integral equation. Numerical results include crack opening displacements, stress intensity factors, and Green’s functions for the entire range of possible periodic crack spacing.

Elastic-Plastic J and COD Estimates for Circumferential Through-Wall Cracks Between Elbows and Straight Pipes Under Bending

2007 ◽  
Author(s):  
Tae-Kwang Song ◽  
Yun-Jae Kim
Keyword(s):  
Crack Opening ◽  
Small Strain ◽  
Opening Displacement ◽  
Limit Loads ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Reference Stress ◽  
Plastic Materials ◽  
Elastic Perfectly Plastic ◽  
Reference Stress Approach

A method for elastic-plastic fracture mechanics analyses is presented for the circumferential through-wall crack in weldment joining elbows and attached straight pipes, subject to in-plane bending, based on the reference stress approach. Based on small strain finite element limit analyses using elastic-perfectly plastic materials, closed-form limit loads for circumferential through-wall cracks in between elbows and straight pipes under bending are given. Then applicability of the reference stress based method to approximately estimate J and crack opening displacement (COD) is proposed.

Load Carrying Capacity of Notched CFRP Laminates

2010 ◽  
Vol 430 ◽  
pp. 47-51
Author(s):  
H. Suzuki ◽  
S. Kinugawa ◽  
Hideki Sekine
Keyword(s):  
Carrying Capacity ◽  
Crack Surface ◽  
Crack Opening ◽  
Damage Zone ◽  
Load Carrying Capacity ◽  
Opening Displacement ◽  
Cohesive Stress ◽  
Cfrp Laminates ◽  
Tension Softening ◽  
Load Carrying

On the basis of a micromechanical study, a method for evaluating load carrying capacity of notched CFRP laminates is developed. The damage zone at a notch tip in CFRP laminates is modeled as a fictitious crack with a cohesive stress acting on the crack surface. Then, applying the Weibull weakest link theory to the strength of surviving fiber bundles on the crack surface, we derive the relationship between the cohesive stress and the crack opening displacement, i.e., the tension-softening relation. By incorporating it in a BEM scheme, the load-displacement relationship is simulated. The simulated result for notched CPRP laminates is compared with experimental ones, and it is found that the simulated and experimental results of load carrying capacity are consistent.

Analysis of Two Cracks Vertical to the Isotropic Plane in Transversely Isotropic Bimaterials

2011 ◽  
Vol 90-93 ◽  
pp. 307-310
Author(s):  
Bing Jun Wang ◽  
Hong Tian Xiao
Keyword(s):  
Free Surface ◽  
Half Space ◽  
Interaction Effect ◽  
Crack Surface ◽  
Crack Opening ◽  
Transversely Isotropic ◽  
Infinite Medium ◽  
Isotropic Plane ◽  
Effect Factor ◽  
Distributed Load

This paper analyzed the interaction between two parallel vertical cracks in a transversely isotropic half space by using the boundary element method (DBEM). The crack surface is perpendicular to the free surface and isotropic plane subjected to normal and tangential uniform distributed load respectively. The stress intensity factor (SIF) values of the crack are calculated from the crack opening displacements. And the interaction effect factor of SIF values is employed to quantitatively describe the interaction between two cracks. The variations of interaction effect factor are investigated with the distances between cracks, the side ratios and free surface. Results show that the existence of the free surface exerts more obvious influence on the SIF values of the crack close to free surface in half space than those in infinite medium. But the free surface has almost no influence on the interaction between two cracks.

Crack Opening/Sliding Morphology and Stress Intensity Factor of Slant Fatigue Crack

2005 ◽  
Vol 297-300 ◽  
pp. 697-702 ◽  
Author(s):  
Kenichi Shimizu ◽  
Tashiyuki Torii ◽  
YouLi Ma
Keyword(s):  
Residual Stress ◽  
Stress Intensity Factor ◽  
Fatigue Crack ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Propagation ◽  
Compressive Residual Stress ◽  
Stress Ratio ◽  
Crack Surface ◽  
Crack Opening

For an actual crack growth in structures subjected to the applied stress from the various directions, it is important to study about the fatigue crack propagation behavior under mixed-mode condition. In particular under the condition, crack surfaces tend to contact when the load is applied because of the compressive residual stress distributed near the crack and the zigzag crack surface morphology. In this study, using slant cracks with compressive residual stress induced in mode I fatigue crack propagation under the stress ratio of R= –1 and 0, stress intensity factors (KI)est and (KII)est were evaluated from the measured crack opening and sliding displacements. As a result, the stress intensity factor (KII)est for the crack made under the stress ratio of R= –1 with the slant angle of 45 deg. was decreased owing to the crack surface contact, while (KI)est showed relatively large values in spite of compressive residual stress.

Fully Plastic Plane Stress Solutions for Biaxially Loaded Center-Cracked Plates

1986 ◽  
Vol 53 (3) ◽  
pp. 555-560 ◽  
Author(s):  
S. Jansson
Keyword(s):  
Fracture Mechanics ◽  
Plane Stress ◽  
Deformation Theory ◽  
Crack Opening ◽  
Small Strain ◽  
Tangential Direction ◽  
Mode I ◽  
J Integral ◽  
Biaxial Testing ◽  
Cracked Plates

Numerical values for the J integral of fracture mechanics, crack opening and load-point displacements are given for stationary cracks in thin quadratic plates where the material is assumed to obey a power-law relation. The plates are loaded biaxially in their own plane under plane stress conditions and the solutions are given under the restriction of small strain and deformation theory. The remote boundaries of the plates are kept straight but free to slide in the tangential direction. This approximates the loading conditions for cruciform specimens with thinner center-sections as used in biaxial testing. It also represents a unit cell in a periodically cracked material. The cracks are loaded in Mode I. The present analysis clarifies the influence of load parallel to the crack and the sensitivity of remote boundary conditions on fracture mechanics parameters.

An Eight-Node Hexahedral Finite Element with Rotational DOFs for Elastoplastic Applications

2019 ◽  
Vol 11 (1) ◽  
pp. 54-66
Author(s):  
Ayoub Ayadi ◽  
Kamel Meftah ◽  
Lakhdar Sedira ◽  
Hossam Djahara
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Plastic Zone ◽  
Displacement Vector ◽  
Small Strain ◽  
Benchmark Problems ◽  
Plasticity Model ◽  
Vector Approximation ◽  
Calculation Code

Abstract In this paper, the earlier formulation of the eight-node hexahedral SFR8 element is extended in order to analyze material nonlinearities. This element stems from the so-called Space Fiber Rotation (SFR) concept which considers virtual rotations of a nodal fiber within the element that enhances the displacement vector approximation. The resulting mathematical model of the proposed SFR8 element and the classical associative plasticity model are implemented into a Fortran calculation code to account for small strain elastoplastic problems. The performance of this element is assessed by means of a set of nonlinear benchmark problems in which the development of the plastic zone has been investigated. The accuracy of the obtained results is principally evaluated with some reference solutions.

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