Double Cantilever Beam Geometry Research Articles

A generalized Rivlin–Thomas theory for nucleation of cracks in viscoelastic materials

Recent fracture experiments using the Rivlin–Thomas pure-shear geometry in rubbery viscoelastic materials have suggested nucleation of cracks at a critical stretch, independent on loading rate. For linear material using the rate-independent cohesive model theory, the critical elongation between grips (in a quite general testing geometry) at nucleation is instead monotonically decreasing with rate of up to the square root of the ratio between the instantaneous and relaxed elastic modulus of the material. Shrimali & Lopez-Pamies have made the assumption of a constant critical stretch to develop a theory which contrasts therefore with classical models. However, we further generalize the Rivlin–Thomas theory by assuming an arbitrary relation between nucleation stretch and loading rate, which therefore includes both models as limit cases. We present a simple case of a Double Cantilever Beam (DCB) geometry with linear standard materials, to show an analytical example.

Crack propagation in the Double Cantilever Beam using Peridynamic theory

In this study, Peridynamic (PD) theory is used to model mode-I delamination in unidirectional and multidirectional laminated composites. Experiments are conducted to determine mode-I fracture toughness in a unidirectional carbon-epoxy Double Cantilever Beam (DCB) specimen where the crack propagation remains on the original notch plane. The PD model of the DCB geometry is generated using an in-house pre-processor code in MATLAB and implemented in ABAQUS software. The brittle damage law in the original PD model is modified to a bilinear law to capture progressive softening. PD results are found to be in good agreement with the experimental results in terms of force–displacement curves and crack length. Next, this PD approach is applied to a multidirectional angle-ply DCB specimen. The PD model shows that delamination path jumps between the layers as the delamination grows. Force–displacement behaviour and delamination patterns obtained using PD model are compared with the corresponding experimental results from Gong et al. (2018). As a result, PD theory with bilinear softening law is found to successfully capture force–displacement relations and delamination migration in multidirectional laminated composites under mode-I loading conditions.

Double cantilever beam fracture toughness measurement method for glass

AbstractA simple method of measuring Mode I fracture toughness, KIC, of glass using the double cantilever beam (DCB) geometry is presented. An inert atmosphere is created at the crack tip to prevent subcritical crack growth and enable “pinning” the crack while the specimen is loaded to failure. This was achieved experimentally using liquid toluene or a glovebox with dry argon. KIC values measured by this method showed good agreement with published literature values for selected glasses. Applicability of the analytical stress intensity factor solution based on crack length, crack front curvature, and the height of the crack guiding groove are confirmed through experimental data and finite element analysis. The experimentally observed crack front curvature, which leads near the edges for small groove heights and leads in the center for larger groove heights, is predicted from the geometry of the DCB specimen for a linear elastic solid through finite element modeling.

Fracture Toughness of Free-Standing ZrSix Thin Films Measured Using Crack-on-a-Chip Method

In this work, we experimentally measure fracture toughness of free-standing zirconium ZrSiₓ thin films using the crack-on-a-chip method. In this method, fracture toughness is determined from the analysis of cracks, which propagate and arrest in specially designed free-standing test structures. The test structures use a well-known double cantilever beam geometry, which enables crack arrest, and don't require any external force actuation, but instead rely on the internal tensile stress of the tested thin film. To produce the ZrSiₓ test structures, a universal fabrication process was developed and used, which avoids typical issues related to etch selectivity and that can be readily applied for other thin film materials. Unlike in previous studies, which used the crack-on-a-chip method, in this work crack initiation was triggered only after the test structures were fully fabricated, which allowed to avoid the influence of the fabrication process on the extracted toughness values. For this, blunt pre-cracks included in the structures were ``sharpened'' using focused ion beam, which resulted in rapid crack propagation and subsequent crack arrest. Mechanical analysis done by a finite element method to extract the values of fracture toughness, showed that buckling of the free-standing thin film test structures has a strong influence on the results of fracture toughness calculations and therefore cannot be ignored. The fracture toughness of ZrSiₓ thin films was determined to be 2.1±0.13 MPa*m <formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex> $^{0.5}$ </tex> </formula> .

Fracture characterization of overmold composite adhesion

A general testing approach is presented via a fracture mechanics study on the interfacial delamination behavior in overmolded composite materials using a variant of the double cantilever beam (DCB) geometry. Overmolding, a common injection molding process, is used to fabricate asymmetric DCB test specimens with Lexan™ 3414 resin overmolded onto commercially available TenCate Cetex® FST woven glass fiber/polycarbonate laminates. An analytical beam theory model is employed to partition the planar fracture modes at the overmold interface into mode I and mode II components, which are functions of material properties and relative beam thicknesses. Specimen curvature measurements are integrated into the beam theory model to estimate the residual stress effects on fracture mode mixity. We use the overmold thickness as a tunable variable to control fracture mode mixity, and target near mode I fracture conditions, where we find mode I fracture energy ( GIc) values of approximately 1 kJ/m2. Fiber bridging across the failure interface is observed, which is not expected at the nominal polymer/polymer overmold interface. Complementary scanning electron microscopy images of the failure surfaces indicate crack initiation at the overmold interface, followed by a change in locus of failure to the nearby polymer/glass fiber interface in the top layer of the composite laminate. Fiber bridging is observed in all specimens tested over a modest range of mode mixity, including specimens modified to the single leg bending geometry, suggesting that the polymer/glass interface is more susceptible to crack propagation than the desired overmold interface, which likely derives its strength from molecular interdiffusion during the overmolding process.

Crack Growth in Hydrous Soda-Lime Silicate Glass

Stable crack growth was measured for nominal dry and water-bearing (6 wt%) soda-lime silicate glasses in double cantilever beam geometry and combined with DMA studies on the effects of dissolved water on internal friction and glass transition, respectively. In vacuum, a decreased slope of logarithmic crack growth velocity versus stress intensity factor is evident for the hydrous glass in line with an increase of beta-relaxation intensity indicating more energy dissipation during fracture. Further, inert crack growth in hydrous glass is found to be divided into sections of different slope, which indicates different water related crack propagation mechanism. In ambient air, a largely extended region II is observed for the hydrous glass, which indicates that crack growth is more sensitive to ambient water.

Crack propagation in a brittle DCB specimen assessed by means of the Williams’ power expansion

A double cantilever beam geometry has been chosen in order to investigate the importance of the higher-order terms of the Williams’ power expansion for the crack path estimation. The crack propagation has been tested experimentally on a brittle polymethylmethacrylate (PMMA) specimen and although the mode I loading conditions were applied, the crack kinked from its original plane immediately and propagated towards the bottom side of the specimen. It has been shown that this phenomenon is connected to the magnitude and sign of the T-stress and to the level of the constraint generally. In this work, the influence of the third and higher terms of the Williams’ series on the crack propagation is investigated. The generalized form of the well-known maximum tangential stress fracture criterion for determination of the crack propagation angle has been tested and discussed. The observed differences in the crack trajectory of different specimens have been found to be related to the magnitude of the higher-order terms of the stress tensor components at the crack tip.

The use of digital-image correlation to investigate the cohesive zone in a double-cantilever beam, with comparisons to numerical and analytical models

Digital-image correlation (DIC) is used to analyze an adhesively-bonded double-cantilever beam (DCB), and to determine the traction-separation law for a cohesive-zone model. The issues involved with how to extract useful information from the digital data of DIC are addressed. In addition, DIC is used to explore how the cohesive zone evolves, and to determine how the elastic arms deform in response to the loading and to the adhesive. The results of these observations are compared to numerical and analytical models for the DCB geometry. In particular, the well-known concept of root rotation is demonstrated. It is shown that, by combining the effects of shear into an effective root rotation, it is possible to use a simple Euler-beam approximation to describe the compliance of the DCB. The experiments and analysis also illustrate the lesser-known concept that significant compression can occur beyond the tensile region in the cohesive zone ahead of a DCB crack tip. Therefore, for accurate numerical predictions, a cohesive-zone model must incorporate compressive deformation. The DIC results are further used to illustrate the concept of a cohesive-length scale. This is defined in terms of the work done against crack-tip tractions, the opening displacement, the stiffness of the arms, and a characteristic geometrical length. The cohesive-length scale is measured experimentally in this paper, and its magnitude is shown to indicate when linear elasticity can be used to describe the deformation of a DCB geometry. The cohesive-length scale is shown to correlate with both the root rotation and the length of a cohesive zone in a fashion that is very similar to what is predicted analytically by elastic-foundation models. Finally, it is demonstrated that, when used in a cohesive-zone model of the geometry, the experimentally determined traction-separation law gives excellent predictions for the evolution of the cohesive zone and for the deformation of the elastic beams. A very minor discrepancy is associated with in-plane tensile stresses that must develop within an adhesive layer in response to the deformation of the beams.

Development of Composites with a Self-Healing Function

This research aimed to realize experimentally the facilevascular self-healing system in epoxy glass fibre reinforced composite. Using flexiblepolytetrafluoroethylene tubes as removable preforms, the channels were embeddedinto both neat epoxy resin and unidirectional glass-fibre reinforced epoxy laminate.Room temperature curable epoxy resin with a surfactant and an amine-basedhardener were the components of the binary healing agent. The specimens oftapered double cantilever beam geometry were subjected to Mode I fracture tests.Fracture of specimens released the healing agent from channels and triggeredself-healing process of the crack. Tested neat epoxy resin specimensdemonstrated recovery of fracture toughness ca. 70 % after 24 h of self-healingat 50°C. Unidirectional laminate specimens (250×23×1.2 mm) were made by vacuuminfusion method from two layers of glass yarns with 5 embedded channels aligningto reinforcing fibers. The channels were alternately filled with components of thehealing agent and then sealed. It was revealed that the embedded vascularchannels in specimens had very little effect on their elastic modulus. Theexperimental program included multiple three-point bending tests of specimensfor their initial damage and self-healing of specimens during their heat treatmentand following exposure at room temperature. Static and dynamic flexural moduli ofelasticity were determined by three-point bending and cantilever beam vibrationat all stages of the test program. The healing efficiency was evaluated as a relativechange of elastic modulus. The efficiency ca. 30 % was reached during 24 h at50°C and additionally increased up ca. 40 % after more than 3 weeks of roomtemperature exposure. The sealed healing agent was capable of maintaining thecapacity for self-healing for at least six months. The research resultsdemonstrated capacity of the macro-channel approach for self-healing realizationin multifunctional polymer composite materials. DOI: http://dx.doi.org/10.5755/j01.ms.21.1.5354

Autonomous Self‐Healing of Epoxy Thermosets with Thiol‐Isocyanate Chemistry

Thiol‐isocyanate chemistry, combined with a dual capsule strategy, is used for the development of extrinsic self‐healing epoxy materials. It is shown that the amine groups present in the matrix both serve as a catalyst for the addition reaction between a thiol and an isocyanate and as a way to covalently link the healed network structure to the surrounding resin. The tapered double cantilever beam (TDCB) geometry is used for evaluating the recovery of the fracture toughness at room temperature after different healing times. Using manual injection of the healing agents into the crack, a healing efficiency up to 130% is obtained for the EPIKOTE 828/DETA epoxy material. On the other hand, when two types of microcapsules, one containing a tetrathiol reagent and the other a low toxic isocyanate reagent, are incorporated into this epoxy thermoset (20 wt%), a recovery of more than 50% is reached. The influence of parameters such as the amount and core content of the microcapsules on the healing efficiency is investigated. Furthermore, the thiol‐isocyanate chemistry is also tested for an industrial cold‐curing epoxy resin (RIM 135/RIMH 137).

Editorial TS: 2nd international conference on structural adhesive bonding

© A m This special issue of Applied Adhesion Science (AAS) contains selected papers presented at the 2nd International Conference on Structural Adhesive Bonding (AB 2013). AB 2013 was chaired by the two of us and was held in Porto, Portugal during July 4–5, 2013. The goal of the conference was to provide a unique opportunity to exchange information, present the latest results as well as to discuss issues relevant to structural adhesive bonding research today. Approximately 130 papers were presented by researchers from more than 20 countries. In order to share the work presented at the conference, a selection of papers was made which resulted in the present Special Issue. The first paper by Quintino et al. is related to training and qualification of adhesive bonding personnel at the European level by the European Welding Federation (EWF). The courses are offered, namely European Adhesive Engineer, European Adhesive Specialist and European Adhesive Bonder. These courses are useful for companies to benefit from improved competitiveness in the global market place and from an increased likelihood of trouble-free production and service performance of their products. In the next paper, Paiva et al. study the importance of the surface treatment in the peeling strength of joints for the shoe industry. The authors considered the following materials: natural leather, thermoplastic rubber (TR), polyurethane (PU) and a polyurethane non structural adhesive solvent based. This work allows manufacturers of footwear to minimize the number of operations in the manufacture of shoes, while still being capable of satisfying the minimum requirements for the sector. In the third paper, Zhang et al. analysed the strength of adhesive joints of riser pipes in deep sea environment loadings such as external pressure, internal pressure, tension, torsion, bending loadings. The authors conclude that singular stress fields exist around the end of the interface. The riser pipe under external pressure, internal pressure and tension loading is more prone to break than under bending and torque loading. The last paper by Valoroso and De Barros is related to adhesive joint computations using cohesive zones. Numerical results are presented for a double cantilever beam geometry with varying thickness for which bilinear and exponential cohesive laws are considered. The authors conclude that the size of the process zone is found to be quite sensitive to the specimen characteristic size. The preparation of this Special Issue has been an interesting experience for the guest editors. The review process gave a deeper insight into the various aspects of adhesive joints and the chance to discuss in detail the manuscripts directly with the authors. We would like to thank the authors for their patience with the process and the

Adhesive joint computations using cohesive zones

The cohesive zone approach has gained increasing success in recent years for simulating debonding and fracture via finite element methods and is ideally suited for simulating adhesive joints, the potential crack paths being generally known in advance in most cases. In the paper the determination of the size of the so-called cohesive process zone is discussed, i.e. the region wherein the stress and damage state have to be correctly resolved in order to properly quantify the dissipated energy and the load bearing capacity of the structure. An a priori estimate for the size of the active process zone is provided based on the beam on elastic foundation model in which the material parameters of the cohesive law are incorporated. The formulation of the cohesive model in a damage mechanics format is first provided. The beam on elastic foundation model is then recalled and an approximate solution for the cohesive zone length is found that depends on a material length and a geometric parameter as well. Numerical results are presented for a Double Cantilever Beam (DCB) geometry with varying thickness for which bilinear and exponential cohesive laws are considered. The influence of the geometry and of the shape of the cohesive law are put forward in terms of global response and evolution of the cohesive process zone. The size of the process zone is found to be quite sensitive to the specimen characteristic size, whose influence is well captured even using a simplified modeling wherein the original cohesive law is changed into an ideal perfectly brittle one. This leads to fairly good estimates of the size of the cohesive zone compared to finite element results.

Comparative study of fracture appearance in crack tip opening angle testing of gas pipeline steels

The crack tip opening angle (CTOA) experiments were conducted on API X65, X70, X80 and X100 steels using a modified double cantilever beam (MDCB) geometry. The fracture surfaces of the test specimens were examined after fracture tests by optical and scanning electron microscopy. The fracture surfaces of the lower grade X65 and X70 steels had fully ductile features including classic flat and slant fracture characteristics. However, repetitive propagation and arrest of quasi-cleavage in the form of chevron arrow-head fractures was observed on the fracture surfaces of higher grade X80 and X100 steels. Interestingly, the analysis of load-displacement records from the latter steels demonstrated local ragged patterns after the test peak load, associated with the repetitive low energy quasi-cleavage mechanism. Detailed discussion on the micro-fractographs of the tested steels and comparison of the test observations with the only newly published work in this filed conclude the paper.

Characterization of mixed-mode I/II fracture properties of adhesively bonded yellow-poplar by a dual actuator test frame instrument

Abstract Experimental results for the fracture behavior under mixed-mode in-plane loading conditions of adhesively bonded wood specimens are reported. The material systems considered involved yellow-poplar (Liriodendron tulipifera), a hardwood of the Magnoliaceae family, as adherends bonded with two different adhesives, a moisture-cure polyurethane (PU) and a phenol/resorcinol/formaldehyde (PRF) resin. A dual actuator test frame permitted fine scanning of fracture behavior over a full range of mixed-mode I/II levels for double cantilever beam (DCB) geometry specimens. These tests showed that, in the considered material systems, the critical strain energy release rate, c, tends to increase as the mode-mixity of the loading increases. In particular, the increase is steeper in proximity to pure mode II loading for the PRF bonded specimens. The experimental values of c obtained were fairly scattered, as is common when testing wood systems. This variability is due in part to the natural variability of wood but also to other factors such as the orientation of the grain in the bonded beams and variations of bondline thickness. In particular, measurements of adhesive layer thickness were performed. This analysis was implemented with microscopic examination of samples cut from untested DCB specimens, where the bondline had not been disrupted by the test. Although the wood parts were power planed prior to bonding, rather large variations of the adhesive layer thickness were observed: on the order of 1–100 μm for specimens bonded with the PU resin and 10–50 μm for specimens bonded with the PRF resin, which showed somewhat more consistent fracture behavior.

Residual stress pinning of delamination fronts on polymer–metal interfaces

The geometry of delamination fronts between a glassy polymer film and a metal substrate in an asymmetric double cantilever beam geometry is studied. Curved crack fronts are observed when tensile residual stresses are present in the polymer layer. Inward bending of the polymer due to the tensile residual stress locally leads to compressive residual stresses normal to the polymer–metal interface and counteracts the imposed crack opening. This modulates the local toughness at the crack front leading to crack front curvature. It is shown that for subcritical cracks under these conditions the critical energy release rate increases with “age” of the crack tip. It also appears that this ageing depends on the local stress state, and that locations with a higher initial toughness age faster. “Pinning points” with increased energy release rates are found to be associated with crack propagation through the polymer layer and also with local stick-slip movement. It is concluded that on these interfaces that are otherwise homogeneous, a distribution of stresses leads to differing local ageing characteristics and delamination mechanisms. The observations indicate that some macroscopic stick-slip phenomena observed in delamination may be due to inhomogeneous front ageing and movement.

Crack propagation along polymer/non-polymer interfaces

Mechanisms of the propagation of crack fronts along interfaces between a glassy polymer and metal or glass are discussed. Specifically, the systems studied are Poly-Ethylene Terephthalate (PETG) spin-coated on Al, PETG-glass and PETG hot-pressed on Cr-sputtered glass. Cracks studied propagate in an Assymetric Double Cantilever Beam (ADCB) geometry. Dependence of microscopic crack front geometry on propagation speed is found. The local stress state is found to have an impact on macroscopic as well as microscopic crack front geometry. Simple lattice model calculations of propagating crack fronts illustrate the impact of disorder and residual stress state on propagation mechanisms and macroscopic crack front shape respectively.

The influence of bond line thickness and peel arm thickness on adhesive fracture toughness of rubber toughened epoxy–aluminium alloy laminates

The adhesive fracture toughness ( G A) of rubber toughened epoxy–aluminium alloy laminates is studied using two types of peel test, namely fixed arm peel and roller-assisted mandrel peel. In the fixed arm tests, the peel angle is varied in the range 45–135° and in the mandrel peel experiments, the mandrel roller size is selected in order to ensure conformance of the peel arm to the roller during fracture. The principal aims of the study are two-fold: (i) To investigate the influence of adhesive bond line thickness on G A. (ii) To investigate the influence of peel arm thickness on G A. The peel crack growth experiments were complemented with measurements of cohesive fracture toughness using tapered double cantilever beam geometry with a range of values for bond line thickness. Throughout the work, it is important to identify the mode of peel fracture and in particular to establish whether the peel cracks are cohesive (propagating in the adhesive) or interfacial (propagating at the interface between adhesive and substrate). To this effect, confocal laser scanning microscopy was used in order to study the peel arms after testing and to measure the thickness of adhesive coating on the peel arms. The experimental work was conducted on a wide range of laminates where two adhesives with a common substrate were employed.

Initiation and Propagation of Delaminations at the Underfill/Passivation Interface Relevant to Flip-Chip Assemblies

A crucial reliability issue for flip-chip microelectronic assemblies is the mechanical integrity of the various bi-material interfaces present. Understanding the mechanics and physics of adhesion is continually reiterated in the International Technology Roadmap for Semiconductors (ITRS). With current trends in the microelectronics industry pushing for smaller and smaller feature sizes, small-scale delamination and initiation are becoming more of a focus in adhesion studies. Our work looks at the application of a stress singularity approach to the initiation problem at various geometric singularities found at interfaces in flip-chip assemblies. Moreover, we compare the adhesion of the same interfaces using standard fracture mechanics. Specifically, several underfill/polyimide interfaces are tested, in both a standard double cantilever beam geometry and a tensile butt joint geometry. The results show a direct correlation between stress intensity values for both the initiation of delaminations and the propagation of existing delaminations. Modified tensile butt joint geometry testing shows an inverse relationship between singularity strength and overall joint strength.

Co-planar crack interaction in cleaved mica

We have performed a combined experimental and analytical study of cleavage in mica using a double cantilever beam geometry in which a crack induced by a wedge driven into one side of the specimen interacts with a pre-existing, coplanar, internal crack. The internal crack is produced by inserting a fiber into the sample on the cleavage plane. As the wedge-driven crack approaches the internal crack, its growth is retarded by the defect, producing an increase in the apparent fracture resistance. With continued loading, the two cracks coalesce. The experiment has been analyzed using a cohesive zone approach to represent the interlayer adhesion in mica. Analysis of the various stages of the experiment reveal scaling dependencies of the different cohesive zone parameters. The coalescence event has been found to depend on parameters other than the fracture resistance of the interface, making it useful for determining additional parameters in the cohesive description, such as the characteristic opening to failure or the cohesive stress. Analysis of the coalescence event is reproduced with finite element calculations. The interaction experiment allows multiple parameters to be determined in a single experiment using a single sample. In our experiments, we observe an increase in the apparent fracture resistance without introducing additional mechanisms for dissipation. Our results reveal the nature of this pinning mechanism and its strength in terms of cohesive fracture parameters.

Fracture toughness of weft-knitted fabric composites

The mode I inter-laminar fracture toughness of advanced knitted textile composites was investigated. Two complex weft-knitted glass fabrics were selected for the study: a triple rib knit and a Milano knit were impregnated with a tough epoxy resin and tested using a double cantilever beam geometry. For both knitted composites, the influence of the growth direction was studied by investigating crack propagation in both the wale and course directions. The fracture toughness was quantified by determining the critical strain energy release rate ( G IC ) using the modified beam theory. The specimens had to be stiffened with layers of glass woven composites added on top and bottom of the beams. This was necessary in order to avoid plastic deformation of the beams and crack deviation out of the inter-laminar plane. The results clearly showed that knitted fabric composites have exceptional inter-laminar fracture toughness properties, namely, more than 7000 J/m 2 . The origin of the high G IC values, which are superior to woven or UD laminates, lies in the very complex fabric architecture. The three-dimensional loop structure induces various energy consuming mechanisms, which do not occur in other composites. Toughening mechanisms such as crack branching, friction, yarn bridging and breakage were identified using scanning electron microscopy.