Computation of energy release rate components by the use of near-tip stress and displacement distributions

A simple method, called the two-term parameter technique, is introduced for the computation of the energy release rate in specimens made of composite materials. A cracked lap shear specimen with a zero degree stacking sequence was employed. The mode II energy release rate, calculated by the two-term parameter technique, was compared with that determined by using the crack closure method. The results show that the two-term parameter technique is very comparable to the crack closure method and does not require exact information of the stress and displacement distributions at the crack tip to get the energy release rate. Moreover, it is shown that while the crack closure method depends on the crack extension size, the two-term parameter technique is less affected by it.     

Determining buckling strain energy release rate through indentation-induced delamination

An oscillating indentation load was applied to delaminate a diamond-like-carbon film from a silicon substrate. After delamination occurred, a two-stage behavior was exhibited in the load-depth results; then, a three-stage behavior was exhibited after buckling occurred due to a long enough delamination length. After removing the indentation load, the debonding film was single-buckled and suspended over the substrate; thus, the delamination length was obtained via the residual profile. Through analysis of the deflection of the buckled film, the buckling strain energy release rate was evaluated.     

Computations of energy release rate under monotonic and cyclic loading conditions

In case of an elastic–plastic fracture mechanics analysis, the determination of the energy release rate distribution is a crucial point. In the present paper, three numerical techniques: the virtual crack closure technique (VCCT), J-integral and energy derivative technique (EDT), are used to compute the energy release rate in a middle-crack tension specimen with the combined isotropic/kinematic hardening model. The results obtained by these methods are compared with each other under monotonic and cyclic loading conditions. Finally, it comes out that the difference of the VCCT method to the J-integral is rather insensitive to load increasing, especially when the traction >40% of yield stress, however, the deviation of the VCCT and J-integral results are within 10%, suggesting that one may use the VCCT for plastic cracked specimen analysis. The computations show that the EDT provides the same values for the monotonic as the J-integral if the plastic deformations are not large, but for high plastic loading the EDT overestimates the fracture energy. For cyclic loading case, VCCT method offers closer results as the elastic analytical results, also suggesting that the whole plastic dissipated energy in the loading process should be integrated. While EDT method gives the smaller results than the J-integral because of the energy dissipated in the unloading phase is considered in the loading process.     

Strain energy release rate at interface of concrete overlaid pavements

A new method for calculating energy release rate (ERR) at the interface of concrete overlaid pavements is proposed using crack closure and the nodal force technique. This method transforms a 3D pavement system into a 2D interfacial crack model via a theoretical conversion. The interfacial ERRs of steel fibre-reinforced, roller-compacted, polymer-modified concrete overlay pavement subjected to vehicular load were calculated and compared with the measured interfacial fracture toughness of the bi-material. It was found that the ERRs considerably decrease with the increase in overlay thickness and elastic modulus of foundation. Thin overlays (less than 100 mm) should not be considered in overlay pavement design to avoid interfacial delamination induced by heavy vehicular loading. For a typical overlay pavement system subjected to complex vehicular loads, an interfacial crack suffers mainly from damage due to mode-I, opening, compared to mode-II, sliding, while mode-III, tearing damage is negligible.     

A new look at energy release rate in fracture mechanics

The energy balance for fracture in elastic/perfectly plastic solids is examined using the finite element method. An extension-release procedure that gives numerically converged solutions is employed in the numerical simulation of crack extensions in elastic/plastic solids. Increments of work and energy during crack extension are calculated for various loading conditions. Several conclusions are obtained. First, the elastic separation work of creating new crack surfaces is shown to be negligible, indicating that the Griffith-type energy release does not exist. Second, as the yield stress increases, the plastic dissipation work rate associated with crack extension converges to the energy release rate in the limiting elastic solid. The latter result can be adopted to interpret the classical energy release rate in elastic solids as plastic dissipation work rate taken in the limit as the yield stress approaches infinity during crack extension. Lastly, it is shown that the energy release rate obtained according to Irwin's plastic zone adjustment approach is equal to the plastic dissipation work rate for the original crack, provided the plastic zone size is less than 10% of the original crack size.     

On the dynamic energy release rate in functionally graded materials

By using the effective shear modulus and mass density, the influence of functional gradient on dynamic energy release rate is discussed under the condition of constant velocity of crack propagation.     

A sandwich three-point bend specimen for testing mode-I interlaminar fracture toughness for fiber-reinforced composite materials

A sandwich three-point bend specimen has recently been proposed to test mode-I interlaminar fracture toughness for fiber-reinforced composite materials. The test composite consist of a thin layer bonded by two lateral reusable steel bars (Sohn et al. 1995). Some time earlier this specimen configuration was used to test fracture toughness of adhesives (Zdaniewsk et al. 1987). However, formulae for analysing its fracture mechanics parameters such as stress intensity factor and energy release rate can not be found in the literature. The lack of adequate formulae may explain why suitable quantitative analysis using this specimen configuration has not been achieved. In this paper, a simple and effective homogenisation method is used to change the bi-material system, which represents the specimen, into single uniform test material. This physical homogenisation is carried out by geometric change of the cross section of lateral steel parts based on equal deflection rigidity. For the transformed specimen configuration of single uniform material, the corresponding stress intensity factor solution from handbooks is available. Two formulae of stress intensity factor for the sandwich three-point bend specimen are given as upper limit and lower limit respectively, they are plotted with varying elastic tensile modulus mismatch. Then the relation between stress intensity factor and energy release rate, with special consideration of orthotropy of the tested composite material, is used to derive its energy release rate. The specimen and its formulae can also be applied to test other materials such as wood, welded joints (Burstow and Ainsworth, 1995), as well as to test dynamic fracture toughness. This revised version was published online in July 2006 with corrections to the Cover Date.     

Application of the energy release rate approach for delamination growth in Glare

Fatigue crack growth in a fibre metal laminate such as Glare is accompanied by delamination growth at the interface between the aluminium and glass fibre/adhesive layers. To incorporate this delamination growth in crack growth prediction methods, the energy release rate approach is applied to describe the delamination growth rate. Tests were performed to determine the relationship between the delamination growth rate and the calculated energy release rate.     

基于虚拟裂纹闭合技术的应变能释放率分析

基于虚拟裂纹闭合技术(VCCT),建立了复合材料层合板层间裂纹尖端的应变能释放率(SERR)三维有限元计算模型。该模型考虑了裂纹尖端大转动和离散单元形状变化对应变能释放率计算的影响,修正了裂纹尖端应变能释放率的计算方法。利用该模型计算了裂纹长度为15 mm和35 mm时纯Ⅰ型和纯Ⅱ型的应变能释放率,纯Ⅰ型应变能释放率分别为 207 J/m2和 253 J/m2;纯Ⅱ型应变能释放率分别为 758 J / m 2和 1040 J / m2;计算值与试验值吻合得很好。同时,该模型计算了混合型不同比值 R=(G_Ⅱ/G_Ⅰ+G_Ⅱ)的长裂纹层合板层间断裂过程的应变能释放率,其中Ⅰ型和Ⅱ型应变能释放率计算值与试验平均值的最大误差为 11.4%,最小误差为 0.4%。该模型能有效计算裂纹尖端的应变能释放率。     

Off-axis fatigue crack growth and the associated energy release rate in composite laminates

Stable matrix crack growth behaviour under mechanical fatigue loading has been studied in a quasi-isotropic (0/90/-45/+45)_s GFRP laminate. Detailed experimental observations were made on the accumulation of cracks and on the growth of individual cracks in +45° as well as 90° plies. A generalised plain strain finite element model of the damaged laminate has been constructed. This model has been used to relate the energy release rate of growing cracks to the crack growth rate via a Paris relation.     

Determination of energy release rate and mode mix in three-dimensional layered structures using plate theory

A plate theory-based method for determining energy release rates is presented for general loadings of three dimensional layered structures. Mode decomposition is performed for cases that exhibit an inverse square root singularity and for which certain other restrictions apply. Predictions for energy release rate and mode mix for typical problems are presented and verified by comparison with results obtained by three dimensional finite element analyses.     

Stress concentration formulae useful for any shape of notch in a round test specimen under tension and under bending

In this work stress concentration factors, K_t , for a round bar with a circular-arc or V-shaped notch are considered on the basis of exact solutions for special cases and accurate numerical results. Then, a set of K_t formulae useful for any shape of notch is proposed. The conclusions can be summarized as follows. (i) For the limiting cases of deep (d) and shallow (s) notches, the body force method is used to calculate the K_t values. Then, the formulae are obtained as K_td and K_ts . (ii) On the one hand, upon comparison of K_t and K_td it is found that K_t is nearly equal to K_td if the notch is deep or blunt. (iii) On the other hand, if the notch is sharp or shallow, K_t is mainly controlled by K_ts and the notch depth. (iv) The notch shape is classified into several groups according to the notch radius and notch depth. Then, the least-squares method is applied for the calculation of K_t /K_td and K_t /K_ts . (v) Finally, a set of convenient formulae is proposed that are useful for any shape of notch in a round test specimen. The formulae give SCFs with <1% error for any shape of notch.     

Crack propagation of CCT foam specimen under low strain rate fatigue

The objective of this study is to investigate the effect of holes on the low strain rate fatigue properties of the nickel foam material and to understand the lifetime of this material which is subjected to the repeated loads. Failures of foam materials under single and repeated loads analogous to fatigue are essential to designers and users in military and aerospace structures. The material failure induced by repeated low strain rate loading becomes a critical issue because of significant loss of stiffness and compressive strength in the foam material. Testing methods to study low strain rate (that is, strain rate) fatigue are quite numerous; no single standard testing procedure is defined for studying the low strain rate fatigue property of a material. The increasing application of foam material in aerospace structures, owing to high specific stiffness and strength has attracted a great concern about the high sensitivity to low strain rate damage introduced during manufacture or in service, and the effects of such damage on structural degradation. To investigate this issue, this study sets up an experimental procedure to determine the low strain rate fatigue properties of nickel foam material. This study performs both experimental and numerical investigations to catch the low strain rate fatigue behavior of nickel foam with open-cell type. The experiments are conducted by rod up and down at the strain rate fatigue of loading. The crack length at the specific cycles are measured experimentally by taking pictures with a paper ruler attached on the surface of specimen and these values are apply to the computer simulations as crack seam model. The simulation result of stress intensity factors are compared with a well known theoretical calculation. Design life and probability of failure or survival at specified life can be calculated so that the fatigue life of nickel core material subjected to repeated low strain rate loading is predicted.     

A non-local stress and strain energy release rate mixed mode fracture initiation and propagation criteria

A non-local stress condition for crack initiation and propagation in brittle materials is presented. This condition is expressed in terms of normal and tangential traction components acting on a physical plane segment (damage zone) of specified length. Next, a non-local strain energy release rate criterion is proposed. This condition is based on the assumption that initiation or propagation of cracking occurs when the maximal value of the function of opening and sliding energy release rates reaches a critical value. The value of energy release rates is determined for finite elementary crack growth. Mixed mode conditions are considered, for which both the critical load value and the crack orientation are predicted from the non-local stress and energy criteria, which are applicable to both regular and singular stress concentrations. The effect of non-singular second order term (T_σ-stress) on the crack propagation is discussed.     

The energy release rate of mode II fractures in layered snow samples

Before a dry snow slab avalanche is released, a shear failure along a weak layer or an interface has to take place. This shear failure disconnects the overlaying slab from the weak layer. A better understanding of this fracture mechanical process, which is a key process in slab avalanche release, is essential for more accurate snow slope stability models. The purpose of this work was to design and to test an experimental set-up for a mode II fracture test with layered snow samples and to find a method to evaluate the interfacial fracture toughness or alternatively the energy release rate in mode II. Beam-shaped specimens were cut out of the layered snow cover, so that they consisted of two homogeneous snow layers separated by a well defined interface. In the cold laboratory 27 specimens were tested using a simple cantilever beam test. The test method proved to be applicable in the laboratory, although the handling of layered samples was delicate. An energy release rate for snow in mode II was calculated numerically with a finite element (FE) model and analytically using an approach for a deeply cracked cantilever beam. An analytical bilayer approach was not suitable. The critical energy release rate G _c was found to be 0.04 ± 0.02 J m⁻². It was primarily a material property of the weak layer and did not depend on the elastic properties of the two adjacent snow layers. The mixed mode interfacial fracture toughness for a shear fracture along a weak layer estimated from the critical energy release rate was substantially lower than the mode I fracture toughness found for snow of similar density.     

Fracture mechanics approach to facesheet delamination in honeycomb: measurement of energy release rate of the adhesive bond

Two types of experiments were designed and performed to evaluate the adhesive bond in honeycomb sandwich panels. The tensile bond strength between the facesheet and the core was determined through the flatwise tension test. The fracture toughness of the bond line was measured through the double cantilever beam test. Fracture toughness values varied for different facesheet thicknesses and core materials. Toughness was also different for the bag and tool sides of the panels for all specimen types.     

Crack-tip force method for computing energy release rate in delaminated plates

A new method called the crack-tip force method (CTFM) is derived for computing the energy release rate in delaminated beams and plates. In this method the delaminated plate is divided into two laminates on either side of the plane of delamination. The interaction forces, called crack-tip forces, between the sub-laminates at the crack-tip are computed. The energy release rate is expressed as a quadratic function of the crack-tip forces and the plate compliance coefficients. The CTFM is compared to the virtual crack closure technique (VCCT) as well as to a previously derived method called the strain energy density method using double cantilevered beam specimens as examples. The CTFM is found to be very efficient as the crack-tip forces are part of the solution of finite element analysis of delaminated plates, and they can be readily used to compute the point-wise energy release rate along the delamination front.     

Design and evaluation of soluble ocular drug insert for controlled release of ciprofloxacin hydrochloride

Purpose: Soluble ocular inserts of ciprofloxacin hydrochloride were prepared with the aim of achieving once a day administration. Design: Drug reservoir was prepared using natural hydrophilic polymer viz. gelatin while rate-controlling membrane was prepared using hydrophobic ethyl cellulose. Ocular inserts were evaluated for their physicochemical parameters like thickness, weight uniformity, drug content, percent moisture loss, and percent moisture absorption. The in vitro drug release studies were carried out using Bi-chambered donar receiver compartment model. Since targeted prolong release was observed in formulation CF2 and CF5, these formulations were further subjected to in vivo drug release study using rabbits as an animal model. In vitro drug release kinetic data was treated according to Zero, First, and Higuchi kinetics to access the mechanism of drug release. Results: Correlation between in vitro and in vivo drug release was found to be strong revealing the efficacy of the formulation. Conclusion: Formulation CF5 has achieved target of present study such as increase residence time, prolong drug release, reduction in frequency of administration, and, thus may improve the patient compliance.     

A localised experimental–numerical technique for determining mixed mode strain energy release rates

Composite structures are being used increasingly in the aerospace industry due to their superior specific stiffness and strength. One key issue associated with such structures is delamination, and how to effectively predict this. A new method which is derived from localised test displacement data is presented to determine the mixed mode strain energy release rates of layered structures with a pre-existing crack. Images taken during experimentation of the vicinity of the crack tip are analysed at low load and high load to determine the displacement changes across the load variation. These displacements are applied as boundary conditions to a simple local numerical model including a constraint at the crack tip. The forces and displacements at the crack tip are taken as output data and combined with the Virtual Crack Closure Technique to predict strain energy release rates. Initial validation of the localised experimental–numerical technique (LENT) shows that applying experimental data to a numerical model does give reasonable agreement thus far in the established trends, and hence LENT is promising for use in determining mixed mode strain energy release rates and mode mixity ratios.