Magnetic and electric poling effects associated with crack growth in BaTiO3–CoFe2O4 composite

Magnetoelectroelastic composite possesses the dual feature that the application of magnetic field induces electric polarization and electric field induces magnetization. The poling directions introduced magnetically and electrically can be different in addition to those for the applied magnetic and electric field. Their choices can influence the character of crack growth which could be enhanced or retarded. The details of how the directions of poling and applied field would affect crack initiation and growth are discussed in relation to the volume fraction of inclusions for a BaTiO₃–CoFe₂O₄ two phase composite. The multi-functional aspects of magnetoelectroelastic materials are involved since they entail multi-scaling features. Failure criteria that applies to isotropic elastic materials may not hold for composites exhibiting piezomagnetic and piezoelectric properties. For instance, a negative energy release rate has been obtained for cracks in piezoelectric materials.In view of what has been said with reference to the energy release rate approach, it is desirable to use the strain energy density function as a failure criterion, even if it is only for its positive definiteness character. Physically speaking, it is attractive to have a function that could rank the proportion of energy related to volume and shape change. They determine the proportion of the hard and soft phase of the composite and hence the volume fraction of the constituent. Strength and toughness parameters used for ranking isotropic and homogeneous materials will not apply for anisotropic and/or nonhomogeneous materials if these microstructure effects could not be suppressed to a lower scale and represented as an average at the macroscopic scale. Too much emphases cannot be placed on the need to clarify the multi-scaling aspects of piezoelectric and piezomagnetic materials. Their behavior as affected by the presence of crack-like defects should be understood prior to deciding whether the material characterization approach would be suitable. That is whether simplicity could justify at the expense of conceptual rigor. Much of this would depend on scaling the time and size related to loading and material structure interaction. The magnetoelectroelastic crack model selected in the work to follow perhaps will provide an insight into the complexicity of the state of affairs for treating the finer details of material behavior with rigor.The proposed test model shows that crack growth in the magnetoelectroelastic materials can be suppressed by increasing the magnitude of the piezomagnetic constants in relation to those for piezoelectricity. A more rational means of evaluating the resistance of materials against fracture is thus proposed, particularly when anisotropy and inhomogeneity might be present.     

Mode II fracture behavior of a Zr-based bulk metallic glass

Shear band formation and fracture are characterized during mode II loading of a Zr-based bulk metallic glass. The measured mode II fracture toughness, K_IIc=75±4 MPa√m, exceeds the reported mode I fracture toughness by ∼4 times, suggesting that normal or mean stresses play a significant role in the deformation process at the crack tip. This effect is explained in light of a mean stress modified free volume model for shear localization in metallic glasses. Thermal imaging of deformation at the mode II crack tip further reveals that shear bands initiate, arrest, and reactivate along the same path, indicating that flow in the shear band leads to permanent changes in the glass structure that retain a memory of the shear band path. The measured temperature increase within the shear band is a fraction of a degree. However, heat dissipation models indicate that the temperature could have exceeded the glass transition temperature for less than 1 ms immediately after the shear band formed. It is shown that this time scale is sufficient for mechanical relaxation slightly above the glass transition temperature.     

Analysis on small scale bridging in fibrous monolithic ceramics

Based on shear lag model of interface between fiber and matrix, a new formula that relates the crack opening displacement and bridging force in fibrous monolithic ceramics was constructed under the framework of small scale bridging. This formula was applied to predict the fracture resistance orR-curve response of a three-point bending specimen made of fibrous monolithic ceramics. A parametric investigation on the influences of fiber volume fraction, fiber radius, characteristics of constituents, BN's fracture toughness and specimen's geometry on the bridging forces and fracture resistance in Si₃N₄/BN composite was carried out. The upper and lower limits of theR-curve of Si₃N₄/BN in small scale bridging were derived. This research revealed the role played by the above parameters in the fracture toughness of fibrous monolithic ceramics. Supported by National Natural Science Foundation of China (59632090).     

On ductile fracture initiation toughness: Effects of void volume fraction,void shape and void distribution

This paper studies the effects of the initial relative void spacing, void pattern, void shape and void volume fraction on ductile fracture toughness using three-dimensional, small scale yielding models, where voids are assumed to pre-exist in the material and are explicitly modeled using refined finite elements. Results of this study can be used to explain the observed fracture toughness anisotropy in industrial alloys. Our analyses suggest that simplified models containing a single row of voids ahead of the crack tip is sufficient when the initial void volume fraction remains small. When the initial void volume fraction becomes large, these simplified models can predict the fracture initiation toughness (J_Ic) with adequate accuracy but cannot predict the correct J–R curve because they over-predict the interaction among growing voids on the plane of crack propagation. Consequently, finite element models containing multiple rows of voids should be used when the material has large initial void volume fraction.     

Role of the polymer phase in the mechanics of nacre-like composites

Although strength and toughness are often mutually exclusive properties in man-made structural materials, nature is full of examples of composite materials that combine these properties in a remarkable way through sophisticated multiscale architectures. Understanding the contributions of the different constituents to the energy dissipating toughening mechanisms active in these natural materials is crucial for the development of strong artificial composites with a high resistance to fracture. Here, we systematically study the influence of the polymer properties on the mechanics of nacre-like composites containing an intermediate fraction of mineral phase (57 vol%). To this end, we infiltrate ceramic scaffolds prepared by magnetically assisted slip casting (MASC) with monomers that are subsequently cured to yield three drastically different polymers: (i) poly(lauryl methacrylate) (PLMA), a soft and weak elastomer; (ii) poly(methyl methacrylate) (PMMA), a strong, stiff and brittle thermoplastic; and (iii) polyether urethane diacrylate-co-poly(2-hydroxyethyl methacrylate) (PUA-PHEMA), a tough polymer of intermediate strength and stiffness. By combining our experimental data with finite element modeling, we find that stiffer polymers can increase the strength of the composite by reducing stress concentrations in the inorganic scaffold. Moreover, infiltrating the scaffolds with tough polymers leads to composites with high crack initiation toughness K_IC. An organic phase with a minimum strength and toughness is also required to fully activate the mechanisms programmed within the ceramic structure for a rising R-curve behavior. Our results indicate that a high modulus of toughness is a key parameter for the selection of polymers leading to strong and tough bioinspired nacre-like composites.     

Effect of T-stress on crack growth under mixed mode I–III loading

For a crack subjected to combined mode I and III loading the influence of a T-stress is analyzed, with focus on crack growth. The solid is a ductile metal modelled as elastic–plastic, and the fracture process is represented in terms of a cohesive zone model. The analyzes are carried out for conditions of small scale yielding, with the elastic solution applied as boundary conditions on the outer edge of the region analyzed. For several combinations of the stress intensity factors K_I and K_III and the T-stress crack growth resistance curves are calculated numerically in order to determine the fracture toughness. In all situations it is found that a negative T-stress adds to the fracture toughness, whereas a positive T-stress has rather little effect. For given values of K_I and T the minimum fracture toughness corresponds to K_III = 0.     

Role of inclusion stiffness and interfacial strength on dynamic matrix crack growth: An experimental study

Experimental simulations of dynamic crack growth past inclusions of two different elastic moduli, stiff (glass) and compliant (polyurethane) relative to the matrix (epoxy), are carried out in a 2D setting. Full-field surface deformations are mapped in the crack–inclusion vicinity optically. The crack growth behavior as a function of inclusion–matrix interfacial strength and the inclusion location relative to the crack is studied under stress-wave loading conditions. An ultra high-speed rotating mirror-type digital camera is used to record random speckle patterns in the crack–inclusion vicinity to quantify in-plane displacement fields. The crack-tip deformation histories from the time of impact until complete fracture are mapped and fracture parameters are extracted. The crack front is arrested by the symmetrically located compliant inclusion for about half the duration needed for complete fracture event. The dynamically propagating crack is attracted and trapped by the weakly bonded inclusion interface for both stiff and compliant symmetrically located inclusion cases, whereas it is deflected away by the strongly bonded stiff inclusion and attracted by strongly bonded compliant inclusion when located eccentrically. The crack is arrested by a strongly bonded compliant inclusion for a significant fraction of the total dynamic event and is longer than the one for the weakly bonded counterpart. The compliant inclusion cases show higher fracture toughness than the stiff inclusion cases. Measured crack-tip mode-mixities correlate well with the observed crack attraction and repulsion mechanisms. Macroscopic examination of fracture surfaces reveals much higher surface roughness and ruggedness after crack–inclusion interaction for compliant inclusion than the stiff one. Implications of these observations on the dynamic fracture behavior of micron size A-glass and polyamide (PA6) particle filled epoxy is demonstrated. Filled-epoxy with 3% V_f of PA6 filler is shown to produce the same dynamic fracture toughness enhancement as the one due to 10% V_f glass.     

Multilevel bridged crack model for high-performance concretes

A multilevel bridged crack model is proposed. It reproduces the constitutive flexural response of reinforced concrete members with fibers. Considered are two different reinforcements: the longitudinal bars (primary reinforcement) and the fibers (secondary reinforcement) distributed in the brittle cementitious matrix. The bridging actions exerted by the reinforcements onto the crack faces are assumed to be rigid-perfectly plastic as the primary constituents. Cohesive softening applies to the fibers.From dimensional analysis, the constitutive flexural response is found to depend on three dimensionless parameters. The first , controls the extension of the process zone. The remaining two parameters, referred to as brittleness numbers N_P⁽¹⁾ and N_P⁽²⁾, are related to the reinforcement phases. Specimen size scale is basic to the global structural behaviour. It can range from ductile to brittle as characterized by the two brittleness numbers. They depend on the reinforcement phase of matrix toughness, reinforcement yielding or slippage limit, reinforcement volume fraction and global structural size.     

Magneto-electro-elastic antiplane analysis of a bimaterial BaTiO3–CoFe2O4 composite wedge with an interface crack

The antiplane analysis is made for a bimaterial BaTiO₃–CoFe₂O₄ composite wedge containing an interface crack. The coupled magneto-electro-elastic field is induced by the piezoelectric/piezomagnetic BaTiO₃–CoFe₂O₄ composite materials. For the crack problems, the intensity factors of stress, strain, electric displacement, electric field, magnetic induction and magnetic field at crack tips are derived analytically. Also, the energy density criterion is applied to predict the fracture behavior of the interface crack. The numerical results also show that the energy release rate for a crack in a single wedge is negative.     

Dynamic mechanical and fracture properties of an infiltrated TiC-1080 steel cermet

The dynamic mechanical and fracture properties of a TiC porous network infiltrated with1080 steel are reported. Following infiltration, the cermet is subjected to various heat treatments that affect essentially the steel matrix. Dynamic compression tests show that the heat treatments increase the fracture strength of the cermet. The quasi-static fracture toughness (K_Ic) is also increased by the heat treatments. The dynamic (initiation) fracture toughness (K_Id) is substantially higher (by about a factor of 3) than its static counterpart. Failure mechanisms consist mainly of cleavage of the TiC and matrix grains, along with minor interfacial decohesion. However, dynamic loading induces substantial damage around the crack tip, consisting essentially of cleavage of TiC grains. Microcrak toughnening is believed to be responsible for the high dynamic toughness of the material. The critical microstructural fracture event is thus identified as the spreading of TiC cleavage microcracks into the neighboring steel grains.     

Reduction of<Emphasis Type="Italic">K</Emphasis><Subscript>I</Subscript> and<Emphasis Type="Italic">K</Emphasis><Subscript>II</Subscript> by the shape-memory effect in a TiNi shape-memory fiber-reinforced epoxy matrix composite

Shape-memory TiNi fiber-reinforced/epoxy matrix composites have been fabricated, and the suppression of crack-tip stress intensity and the change in fracture toughness have been systematically investigated. Stress-strain data for these composite specimens with notches at various angles and different crack lengths in the transverse direction have been measured in tensile tests. The stress intensity factor at the crack tip is experimentally determined from photoelastic fringe patterns. The decreases inK values are attributed to the compressive stress field in the matrix induced when the pre-strains of the TiNi fiber contract to their initial length upon heating above the austenitic final temperature. We present the influences of the pre-strain of TiNi fibers and the compressive domain size between a crack tip and fiber on theK value.     

Mode III fracture behavior of laminated composite with edge crack in torsion

A three-dimensional (3-D) finite element analysis was performed on a [90,(+45/−45)_n,(−45/+45)_n,90]_s class of laminated composites under the edge crack torsion (ECT) test configuration. Finite element delamination models were established and formulas for calculating the Mode III fracture toughness from 3-D finite element models were developed. The relations between the interlaminar fracture behavior and various configuration parameters were investigated and the effects of point loads, ends, geometry, Mode II interference, and friction were evaluated. Results showed that with proper selection of ECT specimen configuration and layup, the delamination could grow in pure Mode III in the middle region of the specimen. Specimen end effect played an important role in the ECT test. A Mode II component occurred in the end regions but it did not interfere significantly with the Mode III delamination state. Specimen dimension ratio, layup, and crack length exhibited significant effect on the interlaminar fracture behavior and the calculated strain energy release rates. However, friction between crackfaces was found to have negligible effect on the interlaminar properties.     

Toughness amplification in natural composites

Natural structural materials such as bone and seashells are made of relatively weak building blocks, yet they exhibit remarkable combinations of stiffness, strength and toughness. This performance can be largely explained by their “staggered microstructure”: stiff inclusions of high aspect ratio are laid parallel to each other with some overlap, and bonded by a softer matrix. While stiffness and strength are now well understood for staggered composites, the mechanisms involved in fracture are still largely unknown. This is a significant lack since the amplification of toughness with respect to their components is by far the most impressive feature in natural staggered composites such as nacre or bone. Here a model capturing the salient mechanisms involved in the cracking of a staggered structure is presented. We show that the pullout of inclusions and large process zones lead to tremendous toughness by far exceeding that of individual components. The model also suggests that a material like nacre cannot reach steady state cracking, with the implication that the toughness increases indefinitely with crack advance. These findings agree well with existing fracture data, and for the first time relate microstructural parameters with overall toughness. These insights will prove useful in the design of biomimetic materials, and provide clues on how bone fractures at the nano and microscales.     

Analyses of tensile deformation of nanocrystalline α-Fe2O3+fcc-Al composites using molecular dynamics simulations

The tensile deformation of nanocrystalline α-Fe₂O₃+fcc-Al composites at room temperature is analyzed using molecular dynamics (MD) simulations. The analyses focus on the effects of variations in grain size and phase volume fraction on strength. For comparison purposes, nanostructures of different phase volume fractions at each grain size are given the same grain morphologies and the same grain orientation distribution. Calculations show that the effects of the fraction of grain boundary (GB) atoms and the electrostatic forces between atoms on deformation are strongly correlated with the volume fractions of the Al and Fe₂O₃ phases. In the case of nanocrystalline Al where electrostatic forces are absent, dislocation emission initiates primarily from high-angle GBs. For the composites, dislocations emits from both low-angle and high-angle GBs due to the electrostatic effect of Al-Fe₂O₃ interfaces. The effect of the interfaces is stronger in structures with smaller average grain sizes primarily because of the higher fractions of atoms in interfaces at smaller grain sizes. At all grain sizes, the strength of the composite lies between those of the corresponding nanocrystalline Al and Fe₂O₃ structures. Inverse Hall-Petch (H-P) relations are observed for all structures analyzed due to the fact that GB sliding is the dominant deformation mechanism. The slopes of the inverse H-P relations are strongly influenced by the fraction of GB atoms, atoms associated with defects, and the volume fractions of the Al and Fe₂O₃ phases.     

Degradation of nylon-6/clay nanocomposites in NO<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>

Nylon-6 is an important engineering polymer that, in its fully spherulitic (bulk) form, has many applications in gears, rollers, and other long life cycle components. In 1993, Toyota commercialized a nylon-6/clay nanocomposite out of which it produced the timing belt cover for the Camry. Although these hybrid nanocomposites show significant improvements in their mechanical response characteristics, including yield strength and heat distortion temperature, little is known about the degradation of these properties due to environmental pollutants like NO _x . Nylon-6 fibers are severely degraded by interaction with NO _x and other pollutants, showing a strong synergy between applied load and environmental degradation. While the nanocomposites show a significant reduction in permeability of gases and water due to the incorporation of lamellar clay, their susceptibility to nondiffusional mechano-chemical degradation is unknown. The fracture toughness of these nylon-6/clay nanocomposites increases, not as a function of clay content, but as a function of the volume of nylon-6 polymer chains influenced by the clay lamellae surfaces. Both the clay and the constrained volume offer the nanocomposites some protection from the deleterious effects of NO _x . The time-to-failure at a given stress intensity factor as a function of clay content and constrained volume is discussed along with fracture toughness of the materials.     

Fracture toughness for CNT specimens from numerically obtained critical CTOD values

Many approaches for estimating mode I fracture toughness (K_IC) using circumferentially notched tensile (CNT) specimen have been demonstrated in the literature. In this paper, an effective approach for estimating fracture toughness from the numerical solution of critical crack tip opening displacement (CTOD) is proposed. An elasto-plastic finite element analysis is used to estimate critical CTOD values for CNT specimens. A number of materials are analysed, and the relationship between K_IC and critical CTOD for CNT specimens is obtained. The proposed relationship is validated by comparing the fracture toughness values obtained from the relationship with those obtained experimentally using CNT specimens. The fracture toughness (K_IC) calculated according to this relationship from numerically obtained critical CTOD is found to be in close agreement with the experimentally obtained fracture toughness for the respective materials.     

Fracture strength for a high strength steel bridge cable wire with a surface crack

In this paper, the fracture strength of a cracked suspension bridge wire is determined based on linear elastic fracture mechanics (LEFM). The wire is 5 mm in diameter, with an original ultimate strength of 1725 MPa and ultimate elongation that ranges between 5.5% and 6%. The average value of for the wire fracture toughness, K_C, was recently evaluated by the author. The state of practice is to use the ultimate strength of the cracked wire as obtained from tensile tests. This approach may overestimate the strength of the wire due to possible delamination and crack tip plasticity. A case study for a group of in situ wire breaks retrieved from a suspension bridge cable is presented. The failure analysis is performed based on both the fracture toughness criterion and the net section theory. The fracture toughness criterion produced more realistic results for the fracture strength of the wire. The decline in the fracture toughness and the corresponding reduction in the fracture strength of cracked degraded wire are predicted making use of the strain energy density criterion.     

Stress intensity factor and crack velocity relationship for polyester/TiO2 nanocomposites

The dynamic fracture behavior of polyester/TiO₂ nanocomposites has been characterized and compared with that of the matrix material. A relationship between the dynamic stress intensity factor,K _I and the crack tip velocity,å, has been established. Dynamic photoelasticity coupled with high-speed photography has been used to obtain crack tip velocities and dynamic stress fields around the propagating cracks. Birefringent coatings were used to conduct the photoelastic study due to the opaqueness of the nanocomposites. Single-edge notch tension and modified compact tension specimens were used to obtain a broad range of crack velocities. Fractographic analysis was conducted to understand the fracture process. The results showed that crack arrest toughness in nanocomposites was 60% greater than in the matrix material. Crack propagation velocities prior to branching in nanocomposites were found to be 50% greater than those in polyester.     

An improved experimental method for the determination of the critical stress intensity factor KIc of brittle materials

The critical stress intensity factor K_Ic is determined by a simple and accurate method, using small test specimens and a simple procedure in this paper.Single edge V-notched tension specimens made of PMMA are subjected to a load which is slowly increased until the crack begins to move from the notch tip. During the crack propagation event shadow patterns at the tip of the crack are recorded in a video recorder. Under these loading conditions, the creating real crack propagate slowly until the crack propagation velocity take an abrupt increase and the entire fracture of the specimen takes place. The stress intensity factor which correspond to the transition from the slow to fast crack speed, is the critical stress intensity factor K_Ic and it can be the fracture toughness of the material.The results are accurate and in good agreement with those values of K_Ic which are calculated by approximate theoretical expressions.The purpose of this paper is to introduce an improved, simple and accurate experimental method for the determination of fracture toughness of brittle materials.     

Physical aging and time–temperature behavior concerning fracture performance of polycarbonate

The effects of physical aging on fracture and yielding behavior are polycarbonate are considered. Two groups of Bisphenol A-based polycarbonate, consisted of extruded PC sheets (thickness of 0.25 mm) and injection molded PC bars (thickness of 3.18 mm) are used. These samples were annealed at various temperatures ranging from 60 to 120 °C, for different times varying up to 240 h. For PC sheets the essential work of fracture (EWF) method was used to analyze fracture behavior. The results are compared to the strain energy density with aging time and aging temperature in the ranges investigated. This effect is confirmed by the change in fracture toughness, as measured by three-point bending tests. The concept of fictive temperature (T_f) was used to characterize the degree of aging in the sample. T_f of a glass in an aged state at a time t is defined as the temperature at which the volume would be equal to the equilibrium volume at T_f if the sample were instantaneously removed to that temperature. Differential scanning calorimetry (DSC) was used to determine T_f. The variations of T_f with aging time and aging temperature are in agreement with both the strain energy density measurement and the three-point bending tests. These results contradict the effects of aging on fracture toughness observed by the essential work of fracture approach. The latter showed anomalous regions of increasing fracture toughness with aging, leading to spurious conclusions. The brittle–ductile transition in fracture behavior is analyzed by an activation energy approach. Aging increases the brittle–ductile transition temperature and the effect is more pronounced for the lower molecular-weight sample. Fracture tests also showed a decrease in the entropy with aging, confirming the results observed previously from tension and compression tests.