Bimaterial Specimens Research Articles

Subinterfacial cracks in bimaterial systems subjected to mechanical and thermal loading

The effect of temperature on the propagation paths of subinterfacial cracks is studied. An aluminum/polymethylmethacrylate bimaterial specimen with large mechanical and thermal mismatches is used to investigate the effect of combined thermal and mechanical loads. The stress intensity factor (SIF) generated by mechanical loading in the presence of a temperature gradient is obtained by means of experiment and analyzed using the finite element method. A full-field optical shearing interferometry technique was used to measure the crack tip stress state. The results show that thermal effects can alter the SIFs sufficiently large enough to change the fracture behavior of subinterfacial cracks.

Fracture initiation at three-dimensional bimaterial interface corners

We propose an approach to correlate fracture initiation at three-dimensional bimaterial interface corners based on the existence of a universal singular stress field in the context of linear elasticity. The idea is to correlate fracture initiation with critical values of the stress intensities of the singular fields calculated from a linear elastic stress analysis. The approach is in the spirit of interface fracture mechanics but applicable to a different class of problems, specifically, situations without a preexisting crack and situations where subsequent crack propagation does not necessarily occur along the interface. In order to validate the proposed approach, we designed and fabricated a series of aluminum/epoxy bimaterial specimens that possess well-defined three-dimensional interface corners. They consist of two perfectly bonded square prisms with varying interface dimensions and surface finishes. The specimens were loaded in four-point flexure until fracture initiated at the three-dimensional interface corner. The nominal stress at failure varied significantly with interface dimensions, thus invalidating its use as a fracture criterion. From a rigorous asymptotic analysis of the three-dimensional interface corner stress state, we determined the order of the singularity and the angular variation of the stress and displacement fields. We determined the corresponding stress intensities via full-field finite element analyses of the aluminum/epoxy specimens. Although the measured failure stress varied significantly with interface dimensions, the corresponding critical stress intensity did not, although as expected it varied with interface surface finish. These findings support the use of critical stress intensities to correlate fracture initiation at three-dimensional bimaterial interface corners.

Q-stresses and constraint behavior of the notched cylindrical tensile specimen

A non-linear numerical analysis of sharp-notched cylindrical specimens under tensile loading was performed, and Q-stresses for various crack lengths were derived at a load level equal to the limit load, P 0. Single-material specimens, representing the base metal of a welded joint, and bi-material specimens, representing an overmatched weld at the site of the crack, were modeled. The results show that shallow-cracked specimens behave as in a plane-stress condition, whereas deeply cracked specimens tend to behave in a plane-strain fashion. The presence of a portion of material (weld metal volume fraction=1/3) with different deformation properties has the effect of raising the constraint on the specimen. The limiting ratio of the diameter of the notch, d, to the outer specimen diameter, D, for a change in the constraint behavior of the notched cylindrical specimens, appears to be of the order of d/ D≈0.50.

The mechanical properties of the macro-interface in squeeze cast SiCw/AZ91 magnesium matrix composites

Squeeze casting is one of the most cost-effective methods of fabricating discontinuously reinforced metal matrix composites. One of the advantages of squeeze casting over other fabrication methods of composites, such as powder metallurgy, stir casting, etc, lies in its possibility to fabricate selectively reinforced composites, such as selectively reinforced squeeze cast pistons [1], which is low cost, lightweight and durable. In a selectively reinforced metal matrix composite, the preform is normally only used to strengthen a portion of the casting, and the rest casting is not reinforced. Then, a boundary is introduced between the composite and the matrix zones, which is commonly called the macrointerface [2, 3]. As with the interface between the matrix and the reinforcement in the composite, there also exists discontinuity of mechanical and physical properties at the interface between the matrix zone and the composite zone. Most studies in the field of squeeze cast metal matrix composites have been carried out on the region of the casting containing the preform, very few investigations have been focused on the macrointerface between the matrix zone and the composite zone [2–5]. Discontinuously reinforced magnesium matrix composites have great potential in aircraft and automotive application because of their low density and high specific properties [6]. In our previous works, the interface between SiC whisker and magnesium in squeeze cast SiCw/Mg composites has been studied in detail [7–9]. The main purpose of the study is to evaluate the mechanical properties of the macro-interface in squeeze cast SiCw/Mg composites, which play an important role in the application of selectively reinforced magnesium matrix composites. All the castings were produced by squeeze casting under CO2/SF6 atmosphere. In the matrix-composite system, the matrix alloy is commercial heat-treatable AZ91 magnesium alloy (8.5–9.5% Al, 0.45–0.90% Zn, 0.15–0.30% Mn, 0.20% Si, 0.01% Ni, balance Mg), the reinforcement is β-SiC whisker whose volume fraction in the preform is 20% with silica binder. The preforms were cylindrical with 50 mm diameter and 50 mm height. The mold and the preform are preheated to 500 ◦C. Magnesium melt overheated to 800 ◦C was poured into the preform. The casting pressure exerted was 100 Mpa. The properties of macro-interface were evaluated under tensile test on bimaterial tensile specimens containing the macro-interface at the mid-length of the reduced section. The tensile specimens were dog bone-shaped with gauge length of 15 mm and thickness of 2 mm. The specimens were machined from the casting cylinder, with the tensile axis parallel to the axis of the casting cylinder (direction of squeeze casting). For comparison, the tensile specimens with the same dimensions machined from the matrix zone and composite zone, respectively, were also tested. The fracture surfaces were examined using Hitachi S570 scanning electron microscope (SEM). Fig. 1 illustrates the typical stress-strain curves for the AZ91, SiCw/AZ91 composite and the bimaterial tensile specimen containing macro-interface between AZ91 alloy and SiCw/AZ91 composite zone, respectively. It can be seen that the ultimate tensile strength of the specimen containing the macro-interface is lower than that of the AZ91 matrix alloy. The same result was also obtained on selectively reinforced SiCw/Al composite that the ultimate tensile strength of the specimens containing the macro-interface is lower than that of the matrix alloy [3]. The yield strength, modulus and elongation of the bimaterial specimen containing macro-interface lay between AZ91 matrix alloy and SiCw/AZ91 composite. It suggests that there exists a certain interfacial bond strength between the matrix and composite region, and both the matrix zone and composite zone contribute to the deformation during the tensile test of specimen containing the macro-interface. The deformation behavior at different regions of the specimen containing macro-interface can be characterized by strain gauges pasted in different parts of the bimaterial tensile specimen, as shown in Fig. 2. Fig. 3 shows the stress-strain curves at different parts of the

The mechanical properties of insert-molded poly (ether imide) (PEI)/C fiber poly (ether ether ketone) (PEEK) composites

The mechanical properties of insert-molded poly(ether imide) (PEI)/carbon fiber poly(etheretherketone) (CF PEEK) have been examined. Bimaterial composite specimens were constructed by injecting CF PEEK into a mold containing one-half of a PEI tensile specimen. These PEI/CF PEEK composites retained much of their strength and dimensional integrity at temperatures as high as 200°C. Variations in test speed had little affect on breaking strains or stiffness. For two grades of PEI examined, properties were independent of the molecular weight of the PEI. Ultimate properties and fracture surfaces suggested good adhesion between the PEI and CF PEEK, possibly aided by miscibility between the two materials. The PEI/CF PEEK bimaterial composites behaved similarly to PC/CF PEEK specimens, but exhibited higher breaking stresses and moduli, both at room and elevated temperatures.

Experimental and Numerical Studies on Crack Kinking Phenomena in Bimaterial Specimen(Crack Growth)

An investigation was undertaken into the interfacial crack kinking phenomena in a bimaterial specimen of epoxy and aluminum alloy using a combination of experimental method and numerical simulation. It was found that all kinked fractures occurred at loading angles equal to or larger than 120°, and this was attributed to the direction of the global shearing mode. Three categories of fracture pattern were identified (A, B and C). In the case of type A fracture, the (J_1^0)_<kink> integrals were generally higher than the homogeneous epoxy J_<ic> at loading angles of 120° and above. In contrast, for types B and C fracture, the J_1^0 integrals were consistently lower than the homogeneous epoxy J_<ic>. Predictions of crack kinking behavior made using the Maximum Energy Release Rate Criterion (MG-criterion) were found to agree well with the observed experimental results.

Measurement of the Near-Field of an Interface Crack Tip by the Intelligent Hybrid Method.

In this study, the phase shifting method of moire-interferometry was used to clarify deformation behavior near an interfacial crack tip. In this experiment, a bimaterial specimen of epoxy and aluminum was used. The unwrapped phase distributions obtained by the phase shifting method of moire-interferometry were automatically wrapped and converted to continuous displacement distributions by using image processing. The measured displacement data were used as the input data of the intelligent hybrid method, which was previously developed by the authors. The intelligent hybrid method successfully demonstrated to obtain smooth higher-order quantities such as the stresses and the strain energy density, automatically detecting and eliminating errors and noises in the experimentally measured displacement fields. Furthermore, for the interfacial crack tip, the path independent separated J integrals useful for interfacial fracture mechanics were actually evaluated. The mixed-mode stress intensity factors were also extracted using the component separation method of the J integral.

Preliminary Examination of the Thermophysical Bond of Insert-molded Poly (Carbonate)/C Fiber Composites

The adhesive strength of a thermophysical bond between two polymers has been examined using fracture mechanics. Bimaterial composite specimens were constructed by injecting C fiber poly(etheretherketone) (PEEK) into a mold containing one-half of a pre-molded poly(carbonate) (PC) dogbone. The resulting specimens were notched at the interface and tested in tension. Adhesion of the two materials was reasonably good, as demonstrated by fracture surfaces that showed a mixture of PC and C fiber PEEK fragments. Interfacial fracture energy of the composite was approximately 1.5kJ/m2.

Cohesive zone modeling of crack nucleation at bimaterial corners

The prediction of crack nucleation from bimaterial corners that have the same corner angle (and therefore singularity) via stress intensity factors is fairly well established. The objective of this work was to examine crack nucleation from a range of corner angles and see if a more general crack nucleation criterion could be formulated. A series of experiments was conducted using an aluminum-epoxy bimaterial specimen loaded under 4-point bending. In addition to the usual measurements of load and an associated displacement, the displacements near the corner were measured using moiré interferometry. Numerical analyses were first conducted assuming a rigid interface. However, the resulting displacements differed from the measured ones, especially near the corner and along the interface. The interface was then modeled as a separate constitutive entity by incorporating a cohesive zone model in the numerical analysis. Following calibration via an interface crack configuration (zero corner angle), the cohesive zone model yielded displacements that were in good agreement with the measured values for all the other corner angles that were considered. The predicted failure loads were also in good agreement with the experimental results. Thus the consistent nucleation criterion was that the area under the traction-separation curve and its maximum traction (the dominant cohesive zone model parameters) remain the same. The numerical solutions indicated that the plastic deformation in the epoxy was small and that failure was predominantly in opening mode. In addition, the critical vectorial crack opening displacement and mode-mix were independent of the corner angle. Finally, a simple design parameter was proposed for predicting the failure load of a bimaterial specimen with an arbitrary corner angle, based on the failure load of a bimaterial specimen with an interface crack.

The J-integral at Dugdale cracks perpendicular to interfaces of materials with dissimilar yield stresses

The J-integral is applied to a Dugdale crack perpendicular to an interface of materials with equal elastic properties but different yield stresses. It is shown that the integral is path independend with certain limitations to the integration path. Three essentially different paths can be distinguished. The first integration path is totally within the first material, it provides the local crack driving force. Performing the integral around the plastic zone in both materials gives the global crack driving force. An interface force can be defined by evaluating the integral along both sides of the plastically deformed region of the interface. A comparison of these three integrals reveals that the global crack driving force is equal to the sum of the local crack driving force and of the interface force. The derived expression for the J-integral are compared with the crack tip opening displacement published recently. This reveals that the local J describes the plastic deformation at the crack tip. Therefore it represents the crack driving force in bimaterials as it does the conventional J-integral in case of homogeneous materials. The analyses are also extended to cyclic plasticity, where an out-of-phase effect is observed. Finally it is discussed how these results can be used to explain fatigue tests at bimaterial specimens.

Examination of the thermophysical bond of insert-molded PC/C fiber composites

The adhesive strength of a thermophysical bond between two polymers has been examined using fracture mechanics. Bimaterial composite specimens were constructed by injecting C fiber polyetheretherketone (PEEK) into a mold containing one-half of a polycarbonate (PC) dogbone. The resulting series specimens were notched at the interface and tested in tension. Adhesion of the two materials was reasonably good, as demonstrated by fracture surfaces that showed a mixture of PC and C fiber PEEK fragments. Interfacial fracture energy of the composite was approximately 1.5 kJ/m2, which is comparable to the cohesive strength of amorphous commodity polymers. Variations in test speed (below the glass transition temperature of the two components, approximately 140°C) had no appreciable affect on stiffness or fracture energy. However, fracture energies decreased slightly as temperature increased.

Dynamic response of bimaterial and graded interface cracks under impact loading

The interfacial fracture in bimaterial and functionally graded material (FGM) under impact loading conditions is investigated using experimental and numerical techniques that are valid for both type of interfaces. Experiments are conducted on epoxy based specimens in three point bend configuration and the complex SIF is measured using an electrical strain gage mounted close to the crack-tip. A complementary two-dimensional finite element simulation is performed using tup force and support reactions as input tractions, and the SIF-time history is determined using a displacement extrapolation technique. The experimentally determined SIF-histories match closely with numerical simulation up to the time of fracture initiation. The test results show that the mode-mixity remains nearly constant through out the test in both the materials, and the mixity values correspond to their respective static counterparts. The general dynamic response of the bimaterial and FGM specimens in terms of impact load, support reaction and the magnitude of complex SIF are comparable, and the mode-mixity is the parameter that distinguishes the graded interface from the bimaterial case.

Measurements of Near-Tip Displacement Fields, Separated J Integrals and Separated Energy Release Rates for Interfacial Cracks Using Phase-Shifting Moire Interfrometry.

In this paper, first, the concepts of the separated J integrals and the separated energy release rates, which have the physical significance of the energy release rates from corresponding material sides of a bimaterial are briefly presented. Phase-shifting moire interferometry is used to investigate interfacial crack-tip behavior of a bimaterial specimen, which is fabricated of epoxy and aluminum. The loading angle to the interfacial crack is systematically changed. The inplane displacement fields near the interface crack are recorded by the phase-shifting moire interferometry. Using the measured displacement fields, the stress intensity factors and the separated energy release rates are evaluated. From the theoretical and experimental results, it is found that the compliant material (epoxy) side provides considerably larger fracture energy to the interfacial crack tip.

Evaluation of interfacial fracture toughness of a flip-chip package and a bimaterial system by a combined experimental and numerical method

In this paper, the interfacial fracture toughness of a flip-chip package subjected to a constant concentrated line load and a bimaterial system under thermal loading condition were evaluated using a unique six-axis submicron tester, a thermal vacuum chamber and FEM modeling coupled with a high density laser moiré interferometry. The six-axis submicron tester was used to provide a constant concentrated line load, whereas the moiré interferometry technique was used to monitor the crack length during the test. In addition, a finite element technique was simultaneously used to determine the near crack tip displacement fields of the specimens. The interfacial fracture toughness and phase angle were computed by using these near tip displacement variables through the analytical energy release rate and phase angle expressions derived by authors. The interfacial fracture toughness and the phase angle of the flip-chip package considered at the interface where the passivated silicon chip meets the underfill are 35 J/m 2 and −65°, respectively, while the interfacial fracture toughness and the phase angle of the tested bimaterial specimen at the interface of the molding compound/silicon with the crack length of 3.3 mm under the temperature rise thermal load from room temperature (20°C) to 138°C are 20.02 J/m 2 and −54.8°, respectively.

A strain gage method for determination of fracture parameters in bimaterial systems

A simple technique for complex stress intensity factor (SIF) determination in a bimaterial crack using electrical strain gages is developed. The asymptotic radial and hoop strain equations are used to compute the SIF by linear transformation. The location of the strain gage relative to the crack tip is chosen through parametric study of the asymptotic fields. The need for higher order terms of the series solution to describe the strain distribution at the gage location is discussed, and a correction procedure using higher order terms is introduced. Static and dynamic experiments are conducted on epoxy/glass-filled epoxy bimaterial specimens in three point bend configuration. Under static loading conditions, the complex SIF estimated from the measured strains is in good agreement with the finite element results obtained by extrapolation of crack flank displacements. The applicability of the present method for dynamic loading conditions is demonstrated by conducting impact tests in a drop-tower system and comparing the measured data with dynamic finite element analysis. The measured dynamic SIF-time history matches favorably with the numerical simulation.

Internal Friction in Bi-material Specimens

A new kind of bi-material specimen is employed in an inverted torsion pendulum to study the internal friction in liquids, and especially in materials during liquid-solid or solid-liquid transitions. Vibration systems containing a bi-material specimen with a solid or a liquid inner material can be described by using a modified three-parameter mechanical model. The theoretical results agree well with experimental data.

Modelling of plane strain interfacial fracture in incompressible materials

Abstract Numerical modelling of a photoelastic experiment is discussed. The experiment examined incompressible materials under plane strain conditions, which results in a simplified analysis owing to a vanishing of the bimaterial parameter. The photoelastic experiment used the stress freezing method to determine near tip stresses in interfacial cracks in bimaterial specimens. Different crack orientations were used to produce different mode mixities. Photoelastic fringe patterns were analyzed to determine the magnitude and phase angle of the complex stress intensity factor. These experiments were modeled using a finite element analysis to determine the field variables near the tips of the interfacial cracks. Magnitudes of the complex stress intensity factors are found from J integral values, derived using the domain integral approach, and the phase angles are determined using extrapolation of the bond line traction data to r =0. The results show that this approach is a useful way to characterize completely the complex stress intensity factor in incompressible linear elastic bimaterial combinations under plane strain conditions.

A methodology for measuring interface fracture properties of composite materials

A methodology is presented for measuring interface fracture properties of composite materials. A bimaterial Brazilian disk specimen with a crack along the interface is employed. The specimen is analyzed by means of the finite element method and a conservative integral to determine stress intensity factors as a function of loading angle and crack length. A weight function is employed to determine the effect of residual curing stresses on the stress intensity factors. These are combined to determine the critical interface energy release rate \(\mathcal{G}\)ic as a function of stress intensity phase angle Ψ for tests carried out on a glass/epoxy material pair.

Influence of material properties of SIFs determined by frozen stress

In a prior study utilizing two materials for which thermal and mechanical properties of both materials in bimaterial specimens were matched except for modulus, it was found that modulus mismatch had a negligible effect on the stress intensity factor (SIF) level and distribution for cracks in bond lines of stress frozen photoelastic bimaterial specimens. However, bond line residual stresses increased the SIF values. Since it is almost impossible to obtain commercial stress freezing materials with matching critical temperatures ( T c) with different moduli, the present study of cracks parallel to and within bond lines utilized such materials with T c mismatch and compared results with parallel studies with matched T c values in order to evaluate T c mismatch effects. Results show that T c mismatch creates mixed mode conditions in cracks parallel to the bond line with significant increases in the mode I SIF ( K 1) for cracks very near the bond line but shows little effect for cracks within or away from the bond line. The absence of a modulus mismatch effect is again confirmed as well.

Opening-mode dominated crack growth along inclined interfaces: Experimental observations

This experimental study investigates the dynamic decohesion of inclined interfaces between aluminum and a polymeric material PSM-1. Two lead azide explosive charges are detonated to initiate dynamic loading in a specially designed bimaterial specimen. The dynamic loading results in crack initiation, propagation and arrest in the same experiment. Photoelasticity, in conjunction with high-speed photography, is used to observe the dynamic event. Dynamic complex stress intensity factor and the energy release rate histories are obtained using the available steady-state singular stress field equations. The dependence of the dynamic initiation and arrest toughness on the mixity under dynamic loading is also investigated. Mixity at crack initiation is controlled by the inclination of the interface. The results show that the initiation toughness is higher than the arrest toughness by about 21%. Based on the experimental observations, a dynamic fracture criterion for subsonic crack growth along the bimaterial interfaces is proposed. According to this criterion, the displacement at a point behind the crack tip varies exponentially with the crack-tip velocity (0 < v < cs; where cs is the shear wave speed of the compliant material). This criterion establishes a generalized relationship between the dynamic energy release rate and the instantaneous crack-tip velocity.