Cohesive Laws for Delamination of CFRP: Experiments and Model

2010 ◽  
Author(s):  
Ulf Stigh
Keyword(s):  
Mixed Mode ◽  
Mode I ◽  
J Integral ◽  
Small Length ◽  
Cohesive Law ◽  
Small Length Scale ◽  
Reinforced Composite ◽  
Dcb Specimen ◽  
Cohesive Laws ◽  
Mode Ii Loading

In the present paper, we study delamination of a carbon fibre reinforced composite at a small length scale, i.e. without consideration of crack bridging. The study is performed within the framework of cohesive modelling. We propose methods based on the applications of the path independent J-integral to measure the cohesive law for delamination. With a DCB-specimen, the cohesive law corresponding to mode I loading is measured and with an ENF-specimen, the law corresponding to mode II loading is measured. These laws are used to calibrate a mixed-mode cohesive law. It is argued that the most important parameters of a cohesive law are the ability to provide the correct fracture energy and strength. The cohesive law is developed using a minimum of adjustable parameters to provide a transparent calibration process.

scholarly journals Direct Evaluation of Mixed Mode I+II Cohesive Laws of Wood by Coupling MMB Test with DIC

Materials ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 374
Author(s):  
Jorge Oliveira ◽  
José Xavier ◽  
Fábio Pereira ◽  
José Morais ◽  
Marcelo de Moura
Keyword(s):  
Mixed Mode ◽  
Crack Tip ◽  
Linear Functions ◽  
Image Correlation ◽  
Bending Test ◽  
Mode I ◽  
Cohesive Law ◽  
Crack Tip Opening Displacement ◽  
Direct Evaluation ◽  
Cohesive Laws

Governing cohesive laws in mixed mode I+II loading of Pinus pinaster Ait. are directly identified by coupling the mixed mode bending test with full-field displacements measured at the crack tip by Digital Image Correlation (DIC). A sequence of mixed mode ratios is studied. The proposed data reduction relies on: (i) the compliance-based beam method for evaluating strain energy release rate; (ii) the local measurement of displacements to compute the crack tip opening displacement; and (iii) an uncoupled approach for the reconstruction of the cohesive laws and its mode I and mode II components. Quantitative parameters are extracted from the set of cohesive laws components in function of the global phase angle. Linear functions were adjusted to reflect the observed trends and the pure modes (I and II) fracture parameters were estimated by extrapolation. Results show that the obtained assessments agree with previous experimental measurements addressing pure modes (I and II) loadings on this wood species, which reveals the appropriateness of the proposed methodology to evaluate the cohesive law under mixed mode loading and its components.

J-Integral Evaluation of Single-Edge Notched Specimens under Mixed-Mode I/II Loading

2001 ◽  
Vol 29 (3) ◽  
pp. 239 ◽  
Author(s):  
DR Petersen ◽  
RE Link ◽  
CD Donne ◽  
A Pirondi
Keyword(s):  
Mixed Mode ◽  
Mode I ◽  
J Integral ◽  
Single Edge ◽  
Integral Evaluation ◽  
Notched Specimens

Measurement of Cohesive Laws and Related Problems

2009 ◽  
Author(s):  
Ulf Stigh ◽  
K. Svante Alfredsson ◽  
Anders Biel
Keyword(s):  
Cohesive Zone ◽  
Adhesive Layer ◽  
J Integral ◽  
Material Behaviour ◽  
Cohesive Law ◽  
Simple Method ◽  
Process Region ◽  
Path Independence ◽  
Cohesive Laws ◽  
Separation Relation

Cohesive modelling provides a simple method to introduce a process region in models of fracture. It is computationally attractive since it blends into the structure of finite element programmes for stress analysis. The development of computational methods and applications of cohesive modelling has accelerated during recent years. Methods to measure cohesive laws have also been developed. One class of such methods is based on the path-independence of the J-integral. By choosing a path encircling the cohesive zone, J can be shown to be given by the area under the traction-separation relation for the cohesive zone. Using an alternative path, J can in some cases be directly related to the applied load and deformation with relatively modest or no assumptions on the material behaviour. Thus, the cohesive law can be measured. Methods to measure cohesive laws for different specimen geometries are presented. The methods are used to measure the cohesive law in peel, shear and mixed-mode for an adhesive layer. A new method to measure cohesive laws in shear is presented. The method is shown to give accurate data with a much smaller test specimen than earlier methods.

On Approximately Realizing and Characterizing Pure Mode-I Interface Fracture Between Bonded Dissimilar Materials

2011 ◽  
Vol 78 (3) ◽  
Author(s):  
Zhenyu Ouyang ◽  
Gefu Ji ◽  
Guoqiang Li
Keyword(s):  
Mixed Mode ◽  
Dissimilar Materials ◽  
Interfacial Fracture ◽  
Interface Fracture ◽  
Mode I ◽  
Mode Ii ◽  
Pure Mode ◽  
J Integral ◽  
Mode I Fracture ◽  
Fracture Behaviors

Bimaterial systems in which two dissimilar materials are adhesively joined by a thin adhesive interlayer have been widely used in a variety of modern industries and engineering structures. It is well known that interfacial fracture is the most common failure mode for these bimaterial systems. Particularly, the interface fracture is a mixed mode in nature mode-I (pure peel) and mode-II (pure shear) due to the disrupted symmetry by the bimaterial configuration. Obviously, characterizing individual fracture modes, especially mode-I fracture, is essential in understanding and modeling the complex mixed mode fracture problems. Meanwhile, the J-integral is a highly preferred means to characterize the interfacial fracture behaviors of a bimaterial system because it cannot only capture more accurate toughness value, but also facilitate an experimental characterization of interfacial traction-separation laws (cohesive laws). Motivated by these important issues, a novel idea is proposed in the present work to realize and characterize the pure mode-I nonlinear interface fracture between bonded dissimilar materials. First, a nearly pure mode-I fracture test can be simply realized for a wide range of bimaterial systems by almost eliminating the mode-II component based on a special and simple configuration obtained in this work. Then, the concise forms of the J-integral are derived and used to characterize the interfacial fracture behaviors associated with classical and shear deformation beam theories. The proposed approach may be considered as a promising candidate for the future standard mode-I test method of bimaterial systems due to its obvious accuracy, simplicity, and applicability, as demonstrated by the numerical and experimental results.

J-Integral Estimation of Circumferential Crack in Round Steel Bar under Mixed Mode (I+III) Loading

2000 ◽  
Vol 2000.3 (0) ◽  
pp. 55-56
Author(s):  
Keisuke TANAKA ◽  
Yoshiaki AKINIWA ◽  
Hirohisa KIMACHI ◽  
Huchen YU
Keyword(s):  
Mixed Mode ◽  
Mode I ◽  
J Integral ◽  
Circumferential Crack ◽  
Steel Bar ◽  
Integral Estimation

scholarly journals Fatigue Crack Growth under Non-Proportional Mixed Mode Loading in Rail and Wheel Steel Part 1: Sequential Mode I and Mode II Loading

2019 ◽  
Vol 9 (10) ◽  
pp. 2006 ◽  
Author(s):  
Makoto Akama
Keyword(s):  
Crack Growth ◽  
Growth Rates ◽  
Mixed Mode ◽  
Crack Tip ◽  
Wheel Steel ◽  
Mode I ◽  
Mode Ii ◽  
Mode Ii Loading ◽  
Crack Growth Rates ◽  
Branch Crack

Fatigue tests were performed to estimate the coplanar and branch crack growth rates on rail and wheel steel under non-proportional mixed mode I/II loading cycles simulating the load on rolling contact fatigue cracks; sequential and overlapping mode I and II loadings were applied to single cracks in the specimens. Long coplanar cracks were produced under certain loading conditions. The fracture surfaces observed by scanning electron microscopy and the finite element analysis results suggested that the growth was driven mainly by in-plane shear mode (i.e., mode II) loading. Crack branching likely occurred when the degree of overlap between these mode cycles increased, indicating that such degree enhancement leads to a relative increase of the maximum tangential stress range, based on an elasto–plastic stress field along the branch direction, compared to the maximum shear stress. Moreover, the crack growth rate decreased when the material strength increased because this made the crack tip displacements smaller. The branch crack growth rates could not be represented by a single crack growth law since the plastic zone size ahead of the crack tip increased with the shear part of the loading due to the T-stress, resulting in higher growth rates.

scholarly journals The J-integral for mixed-mode loaded cracks with cohesive zones

2020 ◽  
Vol 227 (1) ◽  
pp. 79-94
Author(s):  
Johannes Scheel ◽  
Alexander Schlosser ◽  
Andreas Ricoeur
Keyword(s):  
Cohesive Zone ◽  
Mixed Mode ◽  
Cohesive Zone Model ◽  
Crack Tip ◽  
Constitutive Law ◽  
Zone Model ◽  
J Integral ◽  
Cohesive Law ◽  
Crack Tip Opening Displacement ◽  
Opening Displacement

AbstractThe J-integral quantifies the loading of a crack tip, just as the crack tip opening displacement (CTOD) emanating from the cohesive zone model. Both quantities, being based on fundamentally different interpretations of cracks in fracture mechanics of brittle or ductile materials, have been proven to be equivalent in the late 60s of the previous century, however, just for the simple mode-I loading case. The relation of J and CTOD turned out to be uniquely determined by the constitutive law of the cohesive zone in front of the physical crack tip. In this paper, a J-integral vector is derived for a mixed-mode loaded crack based on the cohesive zone approach, accounting for the most general case of a mode-coupled cohesive law. While the $$J_1$$ J 1 -coordinate, as energy release rate of a straight crack extension, is uniquely related to the cohesive potential at the physical crack tip and thus to the CTOD, the $$J_2$$ J 2 -coordinate depends on the solution of the specific boundary value problem in terms of stresses and displacement gradients at the cohesive zone faces. The generalized relation is verified for the Griffith crack, employing solutions of the Dugdale crack based on improved holomorphic functions.

Acoustoelastic Determination of Forces on a Crack in Mixed-Mode Loading

1983 ◽  
Vol 50 (2) ◽  
pp. 379-382 ◽  
Author(s):  
R. B. King ◽  
G. Herrmann
Keyword(s):  
Nondestructive Evaluation ◽  
Mixed Mode ◽  
Experimental Results ◽  
Mode I ◽  
J Integral ◽  
Mixed Mode Loading ◽  
Central Crack ◽  
Ultrasonic Measurements ◽  
Mode I Loading

A technique previously presented [1] for the nondestructive evaluation of the J integral in cracked samples from ultrasonic measurements of stress, and successfully tested on specimens under mode I loading, is extended here to mixed-mode loading. Experimental results are presented for both the J and L integrals in a specimen with a slanted central crack loaded in tension, which agree well with theoretical values.

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