Interface crack initiation at V-notches along adhesive bonding in weakly bonded polymers subjected to mixed-mode loading

In this paper, interface crack initiation at V-notches along adhesive in bonded Polycarbonate (PC) and Poly Methyl Methacrylate (PMMA) subjected to mixed-mode loading conditions was investigated based on a combined experimental, finite element and matched asymptotic analysis. The V-notch specimens with an adhesive interface starting from its tip made at different notch angles were tested under three-point bending conditions. The experimental observations show that the specimens mainly fail by cracks along the interface. Also, the load at the crack initiation increases when the notch angle increases. The computational results are then used to explain and to correlate with the experimental data. A two-fold criterion developed by Leguillon (Eur J Mech A/Solids 21:61?C72 2002) that requires a simultaneous satisfaction of both Griffith energy and stress conditions for the crack initiation at a notch in the specimen made of a homogeneous brittle material is first extended for V-notch specimens under mixed-mode loading conditions and then used to estimate the crack initiation load. The estimated loads appear to agree well with the experimental data. Finally, an inverse method is proposed to estimate the values of fracture toughness at different mode mixity ratios.     

A criterion for brittle fracture in U-notched components under mixed mode loading

A failure criterion is proposed for brittle fracture in U-notched components under mixed-mode static loading. The criterion, called UMTS, is developed based on the maximum tangential stress criterion and also a criterion proposed in the past for mode I failure of rounded V-shaped notches [Gomez FJ, Elices M. A fracture criterion for blunted V-notched samples. Int J Fracture 2004;127:239-64]. Using the UMTS criterion, a set of fracture curves are derived in terms of the notch stress intensity factors. These curves can be used to predict the mixed mode fracture toughness and the crack initiation angle at the notch tip. An expression is also obtained from this criterion for predicting fracture toughness of U-notched components in pure mode II loading. It is shown that there is a good agreement between the results of UMTS criterion and the experimental data obtained by other authors from three-point bend specimens.     

Fracture Assessment of U-Notched Graphite Plates Under Tension

The experimentally obtained tensile load-bearing capacity of fifteen U-notched polycrystalline graphite plates reported in literature was theoretically estimated by means of two well-known brittle fracture models, namely the mean stress (MS) and the point stress (PS) criteria. The results showed that while the mean discrepancies between the experimental and the theoretical results for both the models are very good and approximately equal, the discrepancies are significantly different for various notch tip radii. Meanwhile, the results of MS and PS criteria were compared with the results of the strain energy density (SED) criterion reported in literature. Relatively similar value of mean discrepancy was also obtained for the SED model. It was demonstrated in this research that for small values of the notch tip radius, the MS model is the most appropriate failure criterion while the PS and SED criteria are much better models for medium radii. Moreover, for large notch tip radii, the MS and PS criteria are better choices for tensile fracture assessment of U-notched graphite plates than the SED criterion.     

Multiaxial fatigue of V‐notched steel specimens: a non‐conventional application of the local energy method

The paper deals with the multi‐axial fatigue strength of notched specimens made of 39NiCrMo3 hardened and tempered steel. Circumferentially V‐notched specimens were subjected to combined tension and torsion loading, both in‐phase and out‐of‐phase, under two nominal load ratios, R=?1 and R= 0, also taking into account the influence of the biaxiality ratio, λ=τ_a/σ_a. The notch geometry of all axi‐symmetric specimens was a notch tip radius of 0.1 mm, a notch depth of 4 mm, an included V‐notch angle of 90° and a net section diameter of 12 mm. The results from multi‐axial tests are discussed together with those obtained under pure tension and pure torsion loading on plain and notched specimens. Furthermore the fracture surfaces are examined and the size of non‐propagating cracks measured from some run‐out specimens at 5 million cycles. Finally, all results are presented in terms of the local strain energy density averaged in a given control volume close to the V‐notch tip. The control volume is found to be dependent on the loading mode.     

Thickness effect on crack tip deformation at fracture

The crack tip deformation at the onset of surface crack growth for four single edge cracked specimens having four different thicknesses were studied. The specimens were made of the ductile and tough HY-80 steel. The thickness contraction in the crack tip region and the tensile strain in the direction of load were measured. The crack tip necking-in acts like a notch. The depths, the root radii, and the angle changes of the necking-in notches were measured. The results indicated that the near tip strain can be used as a fracture criterion of ductile and tough materials. It was also found that the fracture strengths of the cracked specimens can be correlated with the tensile ductilities measured with Clausing specimens.     

Sudden Fracture from U-Notches in Fine-Grained Isostatic Graphite Under Mixed Mode I/II Loading

The U-notched maximum tangential stress (UMTS) criterion, proposed originally and utilized previously by the author and his co-researcher for predicting mixed mode I/II fracture in plexi-glass (PMMA) and also pure mode II fracture in PMMA and soda-lime glass, was employed to estimate the experimental results reported in literature dealing with brittle fracture of many U-notched fine-grained isostatic graphite plates under combined tensile/shear loading conditions. By using the fracture curves of the UMTS criterion, which can predict the onset of brittle fracture in terms of the notch stress intensity factors (NSIFs) in the entire domain from pure mode I to pure mode II, the mixed mode fracture toughness (i.e. the load-bearing capacity) of U-notched graphite plates was successfully estimated.     

A finite fracture mechanics approach to structures with sharp V-notches

Criteria assuming that failure of quasi-brittle materials is affected by the stresses acting over a finite distance from the crack tip are widely used inside the scientific community. For instance, they have been applied to predict the failure load of specimens containing sharp V-notches, assuming as a critical parameter the average stress ahead the notch tip. However, this kind of approaches disregards energy balance considerations, which, as well known, are the basis of linear elastic fracture mechanics (LEFM). In order to overcome these drawbacks, the present paper uses a recently introduced finite fracture mechanics (FFM) criterion, i.e. a fracture criterion assuming that crack grows by finite steps. The length of this finite extension is determined by a condition of consistency of both energy and stress requirements; as a consequence, the crack advancement is not a material constant but a structural parameter. The criterion is applied to structures with sharp V-notches. The expression of the generalized fracture toughness, which is a function of material tensile strength, fracture toughness and notch opening angle, is given analytically. Finally, we provide comparisons with: (i) the experimental data we obtained from testing Polystyrene specimens under three point bending; (ii) some experimental data available in the literature. The agreement between theoretical predictions and experimental results is generally satisfactory and, for most of the cases analyzed, the FFM predictions are better than the ones provided by the simple average stress approach.     

Fracture at V-notches with contained plasticity

Fracture at V-notches with contained plasticity was studied. The tested material was a soft annealed tool steel, AISI O1, at −50°C. The material behaviour at this temperature was brittle for a standard fracture toughness test and ductile for a tensile test. Single-edge notched tension and three-point bend specimens were tested, with notch angles ranging from 0° to 140°. For the same notch angle, both brittle and ductile fracture occurred depending on the geometry. However, transferability between different geometries prevailed if the fracture was brittle.Fracture loci derived from simple point-stress or mean-stress criteria were fitted to the experimental results. The trend of the experimental results was followed well even though the fracture loci were derived under the assumption of linear elastic stresses. However, a fracture criterion based on the fracture toughness and a tension test alone will provide a conservative fracture locus.The effect of introducing a notch radius on the used fracture criteria is discussed within the context of linear elastic analysis. As expected, a mean-stress criterion is more sensitive to changes in the notch radius than a point-stress criterion. For both criteria, the sensitivity for changes in the notch radius is less for larger notch angles.     

Fracture initiation at a crack or notch in a viscoplastic material under high rate loading

The two-dimensional problem of an edge crack in a half space or plate is considered. The body is loaded by a suddenly applied, spatially uniform normal velocity imposed on the plane boundary of the body on one side of the edge crack. Otherwise, the boundary of the body, including the crack faces, is traction free. Both cases of an initially sharp crack tip and a narrow notch with small but nonzero notch root radius are considered. The material is modeled as elastic viscoplastic, including strain hardening, rate sensitivity and thermal softening. The applied loading produces predominantly mode II loading in the crack tip region. Under these conditions it is possible to nucleate an adiabatic shear band at the crack tip as a precursor to a mode II fracture. On the other hand, because of the rate sensitivity of the material and the high rate of loading, it may be possible under certain conditions to generate tensile stresses in the crack tip region sufficiently large to nucleate brittle tensile fracture. The problem is solved numerically by means of the finite element method in order to investigate the competition between these two possible fracture initiation mechanisms. The magnitude of the impact velocity imposed on the edge of the plate and the notch tip acuity have an effect on processes near the crack tip. For given material, the inception of crack growth is determined by the competition between a stress-based brittle fracture condition, associated with rate sensitivity and strain hardening, and a strain based criterion, associated with high strain rate and thermal softening.     

Investigation of mixed mode brittle fracture in rounded-tip V-notched components

A criterion is proposed for brittle fracture analysis in rounded-tip V-notched components. This criterion, called RV-MTS, is developed based on the maximum tangential stress (MTS) criterion proposed earlier for investigating mixed mode brittle fracture in sharp cracks. Using the RV-MTS criterion, a set of fracture curves is presented based on the notch stress intensity factors (NSIFs) for predicting mixed mode and also pure mode II fracture toughness of rounded-tip V-notches. The criterion is also able to predict fracture initiation angles under mixed mode loading. The validity of the criterion is evaluated by several fracture tests performed on the rounded-tip V-notched Brazilian disc (RV-BD) specimens made of PMMA. A good agreement is shown to exist between the theoretical predictions and the experimental results for various notch opening angles and different notch radii.     

The cohesive crack concept: application to PMMA at −60 °C

This paper provides a large number of experimental results from the fracture of round-notched samples of a material that remains essentially in the linear elastic regime up to crack initiation. Loading of the samples ranged from pure tensile up to bending. Notch acuity was changed by changing the notch tip radii, notch angle and notch depth. All these experimental results have been used to analyze the predictive capability of the cohesive crack model. All tests were numerically simulated and several criteria justifying the adopted softening function are discussed. The agreement between numerical prediction and experimental results was very good.     

The fracture behaviour of notched specimens of polymethylmethacrylate

The fracture behaviour of notched specimens of polymethylmethacrylate has been examined for a wide range of geometries in Charpy impact tests, and in tensile and slow bend fracture tests. It was found that the failure of the very sharply notched specimens was consistent with linear elastic fracture mechanics and defined a constant fracture toughness K _IC for a constant notch tip radius, whereas the blunt notched specimens failed at a constant critical stress at the root of the notch.     

Effect of an asymmetrical V-notch on the load carrying capacity of eccentrically loaded columns

In this paper theoretical and experimental investigations have been carried out to determine the effect of an asymmetrical V-shaped notch on the load carrying capacity of eccentrically loaded columns. The depth of the notch was kept constant whereas the notch angle, notch root radius; eccentricity of loading and length of the column was varied. It has been concluded that an asymmetrically placed V-notch decreases the load carrying capacity of the column. The load carrying capacity is not affected appreciably upto a notch angle of approx. 90°, but beyond 90° it increases. The load carrying capacity of the column also increases as the notch root radius increases but it decreases as the eccentricity of load and slenderness ratio increase.     

T应力对Ⅰ-Ⅱ复合型裂纹扩展的影响

利用最大周向正应力判据MTS重新分析研究了脆性破坏的Ⅰ-Ⅱ复合型裂纹扩展,其中考虑了平行于裂纹方向的非奇异项T应力。以平板中的斜裂纹处于双向受力为研究对象,通过两个方向力的不同组合以及裂纹与受力方向的夹角变换得到包括纯I型和纯II型在内的Ⅰ-Ⅱ复合型裂纹,分析了T应力对裂纹扩展方向以及断裂时的应力强度因子的影响,并将预测结果与现有的实验数据进行了比较。在此基础上,给出了不同T应力条件下通用的Ⅰ-Ⅱ复合型裂纹扩展条件,可用于给定几何试件的脆性断裂判定。分析结果表明:裂纹尖端非奇异项T应力对裂纹扩展的影响是不可忽略的,尤其是对II型断裂的影响更为明显。     

A new method for evaluating fracture toughness of brittle materials

A new testing procedure is suggested for measuring the fracture toughness of brittle materials as superconductors and ceramics. The idea is to perform a compression test on a subcompact square specimen which contains a central hole. The presence of the hole induces a tensile stress at a certain small region attached to the hole. In this region an artificial notch is introduced such that the fracture path satisfies a pure tensile opening mode (mode I) to which the linear fracture mechanics rules apply. The stress distribution on the fracture plane guarantees a certain amount of stable crack extension. The relationship between the critical compressive load and the stress intensity factor is formulated via an available Green function along with a numerical solution (FEM with ANSYS code). The testing procedure is demonstrated with specimens made of two types of tungsten carbide which differ by their grain size only. Test results are examined via fracture toughness and strength values produced by other conventional methods and the agreement is very good. The geometry and loading direction enable the fracture toughness results to be relatively insensitive to the notch tip radius and the crack length, thereby relaxing the requirements for accurate measurements.The small size of the suggested specimen (12.70mm×12.70mm×5mm) and the avoidance of gripping interfaces provide the major cost-wise advantages.     

Experimental studies on mixed‐mode dynamic fracture behaviour of aluminium alloy plates with narrow U‐notch

Mixed‐mode dynamic fracture behaviour of cast aluminium alloy ZL205A thin plates with narrow U‐notch was studied by split Hopkinson tensile bar apparatus. Specimens with different loading angles were designed to realize different fracture modes. The same loading condition was maintained during the tests. Recovery specimens show that crack propagates along the notch direction. Force–elongation relations show that with the loading angle increasing, the fracture force increases while the final elongation decreases. Deformation and fracture process was observed by a high‐speed camera. Displacement distribution around the crack was calculated through digital image correlation technique. Based on the photos and displacement results, initiation time of the crack was derived. Besides, two stress components (normal stress and shear stress) applied on the fracture surface were investigated. Results show that crack initiation stresses at different loading angles satisfy the ellipse equation. Pure mode I and II fracture stresses are 425.3 and 236.7 MPa, respectively. Furthermore, specific fracture energy of different specimens was calculated. The energy data vary with loading angle and located on an approximate upward parabolic curve. From the curve, the minimum specific fracture energy of the thin plate specimen is 42.0 kJ/m² under loading angle of 76.3°.     

Multi-axial fatigue behaviour of a severely notched carbon steel

The paper deals with multi-axial fatigue strength of notched specimens made of C40 carbon steel (normalised state), subjected to combined tension and torsion loading, both in-phase and out-of-phase (Φ=0 and 90°). V-notched specimens have been tested under two nominal load ratios, R=−1 and 0, while keeping constant and equal to the unity the biaxiality ratio, λ=σ_a/τ_a. All specimens have the same geometry, with notch tip radius and depth equal to 0.5 and 4 mm, respectively, while the V-notch angle is equal to 90°. The results determined are discussed together with those deduced under pure tension or torsion loading on plain and notched specimens as well as on small shafts with shoulders. The application of an energy-based approach allows all the fatigue data obtained from the notched specimens to be summarised in a single scatter band, in terms of the total strain energy density evaluated at the notch tip against cycles to failure.     

A Finite Fracture Mechanics approach to the asymptotic behaviour of U‐notched structures

A Finite Fracture Mechanics (FFM) criterion is formalized to predict the critical failure loads of brittle U‐notched specimens, subjected to mode I loading. The criterion, recently applied to V‐notched structures, requires the contemporaneous fulfilment of stress requirements and energy conditions for fracture to propagate: the stress field ahead of the notch tip and the stress intensity factor related to a crack stemming from the root are involved. Both the apparent fracture toughness and the critical crack advancement result to be structural parameters. For sufficiently slender notches, the root radius becomes the only relevant geometric dimension. The consistency of the approach is proved by the comparison with experimental data available in the Literature.     

Brittle fracture initiation from a blunting crack

Brittle fracture initiation under increasing load occurs from a blunting crack. The present paper proposes as a criterion for the transition from blunting to fast crack growth that the available elastic energy divided by a volume which depends on the fracture mechanism and the crack tip opening displacement reaches a critical value. This criterion is shown to be applicable for initiation from initially sharp cracks, initially rounded notches and from ductile growing cracks. The model allows a quantitative discussion on the size, temperature and notch root radius requirements for fracture mechanics testing.