R-curve Behavior Research Articles

Fracture anisotropy in texturized lithium disilicate glass-ceramics

Lithium disilicate glass-ceramics show great potential in the fabrication of anisotropic structures due to their high-strength needle-form crystalline phase subjective to processing-induced alignment. Here we explore this strategy by focusing on the mechanistic aspects of fracture. Through different variations of the fracture toughness test we demonstrate the effect of bulk crystal orientation on fracture energy, toughening mechanisms, crystal size and aspect ratio. Using the anisotropic Poisson's ratio of the Li2Si2O5 crystal phase obtained by Resonant Ultrasound Spectroscopy, we apply the new geometry factor developed by Strobl et al. to provide a more accurate insight into the anisotropic crack propagation behavior in LS2 glass-ceramics. Raman spectra and X-Ray Diffraction patterns are resolved for the Li2Si2O5 phase aligned at plane parallel, anti-plane and random orientations.We show that Li2Si2O5 crystallites oriented perpendicular to the crack growth plane tended to induce large scale crack deflection unless the crack was forced into a straight path, thereby promoting crystallite fracture, increased KIc-values and accentuated R-curve behavior. Crystal aspect ratio and residual stresses in the glass have been identified as important influencing factors on crack growth behavior and toughening mechanisms.

Strength and reliability of WC-Co cemented carbides: Understanding microstructural effects on the basis of R-curve behavior and fractography

Strength and reliability of WC-Co cemented carbides (hardmetals) are dependent on effective fracture toughness as well as on nature, size and distribution of processing flaws. Regarding toughness, they exhibit a crack growth resistance (R-curve) behavior, derived from the development of a multiligament bridging zone at the crack wake. Accordingly, successful implementation of fracture mechanics requires consideration of tangency criterion, between applied stress intensity factor and R-curve, in addition to fractographic inspection. It is the aim of this study to evaluate the strength behavior of a series of experimental WC-Co grades on the basis of R-curve failure criteria. Results indicate that microstructural effects on the strength of hardmetals may be satisfactorily rationalized following the referred criterion. The analysis includes consideration of nature and distribution of fracture origins, found to be more diverse and wider, respectively, for the harder fine-grained grades. This experimental evidence, together with the fact that these hardmetals exhibit steeper rising R-curves than tougher coarse-grained ones, leads to lower reliability for the former. This investigation documents and validates the great relevance of R-curve behavior for optimizing the mechanical performance of WC-Co cemented carbides on the basis of microstructural design.

A numerical framework to analyze fracture in composite materials: From R-curves to homogenized softening laws

A numerical framework to obtain the crack resistance curve (R-curve) and its corresponding softening law for fracture analysis in composite materials under small scale bridging has been developed. The use case addresses the intralaminar transverse tensile fracture of a unidirectional ply of carbon fiber-reinforced polymer AS4/8552. The R-curve is computed for this material using a micromechanical embedded model corresponding to the intralaminar transverse tensile fracture toughness characteristic. The model combines an embedded cell approach with the Linear Elastic Fracture Mechanics (LEFM) displacement field to analyze the local crack growth problem including fiber/matrix interface debonding and matrix ligaments bridging as the main energy dissipation mechanisms. Other large scale toughening effects as, for instance, fiber bridging were not included in the model. Parametric analysis were carried out to assess the influence of the properties of the material constituents on the R-curve behavior and on the corresponding homogenized cohesive laws.

Strong and tough metal/ceramic micro-laminates

There is a growing interest in the development of composites with complex structures designed to generate enhanced mechanical properties. The challenge is how to implement these structures in practical materials with the required degree of control. Here we show how freeze casting of ceramic preforms combined with metal infiltration can be used to fabricate Al2O3/Al-4wt% Mg micro-laminated composites. By manipulating the solid content of the suspension and the morphology of the ceramic particles (from platelets to round particles) it is possible to access a range of structures with layer thickness varying between 1 and 30 μm and metallic contents between 66 and 86 vol%. The mechanical response of the materials is characterized by combining bending tests with observation of crack propagation in two and three dimensions using different imaging techniques. These composites are able to combine high strength and toughness. They exhibit a rising R-curve behaviour although different structures generate different toughening mechanisms. Composites fabricated with Al2O3 particles exhibit the highest fracture resistance approaching 60 MPa m1/2, while laminates prepared from Al2O3 platelets exhibit higher strengths (above 700 MPa) while retaining fracture resistance up to ∼40 MPa m1/2. The results provide new insights on the effect of structure on the mechanical properties in metal-ceramic composites as well as on the design of appropriate testing procedures.

Influence of porosity on mechanical properties of tetragonal stabilized zirconia

3YSZ specimens with variable open porosity (1–57%) were fabricated, and the stiffness, strength and fracture properties (fracture toughness and R-curve) were measured to investigate their potential use as support structures for solid oxide fuel or electrolysis cells. The ball-on-ring test was used to characterize Young's modulus and Weibull strength. The variation of fracture toughness with porosity was investigated and modelled using the results from fracture mechanical testing. A distinct R-curve behaviour was observed in dense 3YSZ specimens, in samples with a porosity around 15% and in some of the highly porous samples (porosities ∼45%) reflecting a transformation toughening in the material. For the most porous samples, the “R-curve behaviour” disappeared and subcritical crack growth was observed. The studies indicate that even highly porous 3YSZ structures (porosities exceeding 40%) are feasible supports for SOFC/SOECs from a mechanical point of view.

An interface-dependent model of plateau fracture toughness in multidirectional CFRP laminates under mode I loading

Obvious R-curve behavior exists in multidirectional carbon fiber reinforced polymers (CFRP) laminates under mode I loading, in which the plateau fracture toughness represents the steady-state delamination growth behavior. By decomposing the fracture toughness into the fracture work for pure delamination at the interface and that for the intra-ply damage of adjacent layers, a mechanism-based correlation between the plateau value of interface mode I fracture toughness in multidirectional laminates and the interface angle and/or the two angles of the fiber orientations of the two layers surrounding the crack tip was developed, which is an explicitly interface-dependent formula. Static tests were performed on six types of DCB specimen with different interfaces. The analytical calculations agreed well with the experimental data, verifying the proposed correlation. The intra-ply damage and fiber bridging during delamination along different interfaces were evaluated, which provides a justification for the proposed model.

Fracture toughness and R-curve behavior of BCP/YTZP nanocomposites produced using the spark plasma sintering process

The aim of this study is to evaluate the fracture toughness and R-curve behavior of synthesized biphasic calcium phosphate (BCP) and yttria-tetragonal zirconia polygonal (YTZP) nanocomposites produced by spark plasma sintering (SPS) method. BCP comprising of 30 wt% hydroxyapatite and 70 wt% betatricalcium phosphate, was mixed with various amounts of YTZP nanopowder and sintered using SPS at different processing conditions (e.g. various pressures, times, temperatures, cooling and heating rates). Fracture toughness (KIC) of the samples was calculated by the indentation-strength method and the phase composition of the samples was evaluated by x-ray diffractometry (XRD). Transmission electron microscopy (TEM), scanning electron microscopy (SEM) and energy dispersive x-ray (EDX) analyses were also utilized to study the powder morphology, microstructure and fractured surfaces of the samples. According to the results, the bulk density can reach to about 97% of the theoretical density using SPS process. The maximum fracture toughness of 3.04 MPa m0.5 was obtained for the sample containing 3 vol% of YTZP (BCP-3SZ) in optimum conditions of the SPS process. The obtained fracture toughness value was approximately triple of the pure BCP (1.07 MPa m0.5) and was comparable with that of the cortical human bone. Rising crack growth resistance (R-curve) behavior of the sample BCP-3SZ at different indentation loads was also observed due to the martensitic phase transformation. Furthermore, YTZP nanoparticles persuade HA to β-TCP phase transformation during the SPS process.

The effect of residual stress on whisker reinforcements in SiCw-Al2O3 composites during cooling

The effect of residual stress on whisker reinforcements in SiCw-Al2O3 composites from 293 K to 77 K was investigated. The fracture toughness of SiCw-Al2O3 composites measured at 77 K was ∼26% higher than that at 293 K. The calculated compressive stress of SiC whiskers at 77 K was ∼600 MPa, and the local stress distribution is demonstrated by in-situ Raman spectra and fluorescence spectra. R-Curve behaviors and crack opening displacement profiles were determined to compare the effect of residual stress on crack bridging at different temperatures. The experimental results verified that crack bridging was enhanced by residual stress at 77 K, which made the SiCw-Al2O3 composite to be a promising material for cryogenic applications.

Measuring fracture toughness in biological materials.

Many biological materials fail by cracking. Examples are bone fractures, contact damage in eggs, splits in bamboo culm and defects in cartilage. The mechanical property that best describes failure by cracking is fracture toughness, which quantifies the ease with which cracks propagate and defines a material's tolerance for pre-existing cracks and other stress concentrating features. The measurement of fracture toughness presents some challenges, especially for biological materials. To obtain valid results requires care and, in many cases, considerable ingenuity to design an appropriate specimen and test protocol. Common mistakes include incorrect interpretation of the mechanics of loading in unusual specimen designs, and failures occurring at the material's ultimate tensile strength as a result of specimens or cracks being too small. Interpretation of the resulting toughness data may also present challenges, for example when R-curve behaviour is present. In this article, examples of good and bad practice are described, and some recommendations made.

Crack-growth resistance behavior of mode-I delamination in ceramic matrix composites

Mode-I delamination crack growth in Ceramic Matrix Composite (CMC) materials is studied using experiments and associated numerical modeling. Double cantilever beam tests were conducted to measure delamination growth characteristics and the associated mode-I critical energy release rate. The tests revealed significant crack growth resistance (R-curve) behavior with the load carrying capacity increasing with the delamination growth. The experimentally observed load-displacement response could not be explained by linear elastic fracture mechanics or by a two-parameter triangular cohesive finite element models. The observed crack growth resistance behavior is explained by incorporating cohesive traction-separation relationship with a bilinear softening resulting in a long “tail”, which is interpreted and modeled as a superposition of two traction-separation relationships representing mechanisms associated with near crack-tip region and fiber-bridging in the crack-wake, respectively.

R-curve behavior of laminated ZrB2-SiC/Graphite ceramics in two different directions

Laminated ZrB2-SiC/Graphite ceramics were fabricated by tap-casting and hot-pressing sintering. In this study, the R-curve behavior in two different directions was investigated using indentation-strength technique. The flexural strengths in the parallel direction and perpendicular direction were 382MPa and 429MPa, respectively. The indentation strength values first decreased and then increased with increasing the indentation load. When the indentation load was 294 N, the strength reached the maximum value of 360MPa in the parallel direction and 399MPa in the perpendicular direction. The laminated ZrB2-SiC/Graphite ceramics exhibited an evident rising R-curve behavior in both directions, which was mainly attributed to the consumption of fracture energy by crack deflection and crack branching at the weak graphite layers.

On the understanding of the effects of sample size on the variability in fracture toughness of bulk metallic glasses

High strength in combination with improvements in failure characteristics and associated gains in fracture toughness have placed bulk metallic glasses (BMGs) among the most damage-tolerant materials to date. Recent studies show, however, that there can be large variabilities in the mechanical performance of these alloys, particularly in their toughness, which are likely associated with sample-size effects or structural variations from differences in processing. Here, we examine the variation in fracture toughness of the Pd-based metallic glass Pd77.5Cu6Si16.5, using single-edge notched bend specimens but in two different sizes. Although all toughness results on this glass were “valid” in terms of the nonlinear-elastic fracture mechanics J-standard, i.e., one would expect a single value of the fracture toughness for this alloy, marked differences were apparent in the toughness values and failure characteristics of the differently-sized samples. Specifically, significantly larger variations in toughness values were measured in larger-sized samples, which all essentially failed catastrophically, whereas none of the smaller-sized samples failed catastrophically yet displayed far less scatter in their measured toughness. Additional in situ tests on the smaller-sized samples in a scanning electron microscope revealed stable crack growth and progressive resistance to crack extension, i.e., rising crack-resistance (R-curve) behavior. Overall, this marked transition from brittle catastrophic failure in large samples, where a size-independent fracture toughness can be measured, to non-catastrophic, more ductile (R-curve), behavior in smaller samples, the latter associated with higher toughness, is related to the distinct size-dependent bending ductility and strain-softening behavior in BMGs.

A New Method to Measure Crack Extension in Nuclear Graphite Based on Digital Image Correlation

Graphite components, used as moderators, reflectors, and core-support structures in a High-Temperature Gas-Cooled Reactor, play an important role in the safety of the reactor. Specifically, they provide channels for the fuel elements, control rods, and coolant flow. Fracture is the main failure mode for graphite, and breaching of the above channels by crack extension will seriously threaten the safety of a reactor. In this paper, a new method based on digital image correlation (DIC) is introduced for measuring crack extension in brittle materials. Cross-correlation of the displacements measured by DIC with a step function was employed to identify the advancing crack tip in a graphite beam specimen under three-point bending. The load-crack extension curve, which is required for analyzing the R-curve and tension softening behaviors, was obtained for this material. Furthermore, a sensitivity analysis of the threshold value employed for the cross-correlation parameter in the crack identification process was conducted. Finally, the results were verified using the finite element method.

Delamination fracture toughness of continuous glass-fiber/epoxy composites for structural applications

This paper presents experimental results of delamination fracture toughness tests on glass-fiber/epoxy composites which are manufactured in a novel Compression Resin transfer molding (CRTM) process in comparison to the performance of a well-studied RTM reference process. The examined laminates are built out of six plies, with a plain weave fiber orientation. 90% of the fibers are in longitudinal direction and 10% are perpendicular woven in. The influence of the process regarding interlaminar fracture toughness is tested under pure mode I (DCB), pure mode II (ENF) and mixed mode loading (MMB). The aim of this study is to establish a semi-empirical criterion to derive the interlaminar fracture toughness of all mixed-mode ratios using the pure mode I or II loading fracture toughnesses. It has been found, that the materials performance for both processes are comparable, however the fracture behavior is strongly influenced by the fabric structure. The examination of the laminates polymer system showed a strong R-curve behavior for mode I and mode II loading. It was possible to establish a semi empirical criterion that shows good agreement with the experimental results.

A multi-scale based cohesive zone model for the analysis of thickness scaling effect in fiber bridging

A cohesive zone model (CZM) is proposed to assess the thickness scaling effect associated with fiber bridging during fracture. The CZM was developed through a multi-scale simulation approach and utilizes an embedded cell model of the Double Cantilever Beam (DCB) that explicitly accounts for the bridging bundles on the fracture plane. In particular, micromechanical simulations of failure were carried out, for varying arms thickness, in order to determine the homogenized fracture behavior. To model the observed scaling effect, the conventional cohesive law, formulated as an opening-stress relation, is enriched with information on the crack opening angle. Continuum finite element simulations indicated that the proposed CZM was able to mimic very well the essential features observed in the experiments, e.g. raising R-curve behavior and thickness scaling effect on the energy dissipated at steady state.

XFEM-based model for simulating zigzag delamination growth in laminated composites under mode I loading

Interfaces adjacent to a 90° ply in laminated composites show a typical zigzag path during the mode I delamination propagation process, which is considered to be closely related to high propagation values of fracture toughness. DCB (double cantilever beam) tests of specimens with a starter crack inserted into two 90° mid-layers were carried out, during which the zigzag delamination growth and pronounced R-curve behavior were obtained. To simulate the zigzag delamination propagation path, four XFEM-based delamination growth models were proposed which were comprised of a crack initiation model and a crack propagation model, respectively. In the framework of the delamination growth model, a new crack initiation model was developed, which took a quadratic criterion as the crack initiation criterion and the direction orthogonal to the maximum principal stress as the crack growth direction. Based on the mechanism of the delamination resistance, four crack propagation models considering whether the delamination follows a pure or mixed mode damage evolution law and whether a constant or varying critical fracture toughness dominates the damage evolution were introduced. By comparing the predictions from the four delamination growth models and the experimental results, the mode I delamination mechanism with a zigzag path was investigated. The delamination growth model that adopted a critical fracture toughness function and the mixed mode damage evolution law showed the best agreement with the experimental results and was recommended.

Direct observation of toughening and R-curve behavior in carbon nanotube reinforced silicon nitride

The efficacy of toughening in nanoscale ceramic composites is currently controversial, in part because indentation based fracture toughness measurements are not reliable in these materials. To explore the relevant mechanisms, in situ mechanical testing was used to investigate carbon nanotube reinforced silicon nitride. Nanoindentation of microcantilever beams (cut with a focused ion beam) made it possible to probe fracture and notch sensitivity. Stable crack growth was directly observed with this approach. The measured R-curve for these composites was obtained from analysis of these data. These results provide direct evidence of significant toughening enhancements in a carbon nanotube reinforced ceramic composite.

Effect of interface fiber angle on the R-curve behavior of E-glass/epoxy DCB specimens

In this study, the effect of interface fiber angle on the R-curve behavior of double cantilever beam (DCB) specimens made of E-glass/epoxy under mode I loading is investigated experimentally. For this purpose, DCB specimens with stacking sequences of [011/θ//012] and θ=0, 30, 45, 90 are manufactured by hand lay-up method. These stacking sequences are chosen to eliminate the effect of remote ply orientation on the R-curve behavior of DCB specimens during the delamination propagation. In order to obtain the critical strain energy release rate, fracture tests are conducted on these specimens. Results show that DCB specimens with 0°//0° interface have the lowest initiation interlaminar fracture toughness and the greatest bridging zone length due to good penetration of two adjacent layers of the delamination interface. Moreover, results indicate that the interface fiber angle has significant effect on the steady-state interlaminar fracture toughness as well as the bridging zone length.

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 (57vol%). 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 KIC. 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.

R-Curve Approach to Describe the Fracture Resistance of Tool Steels

This work addresses the events involved in the fracture of tool steels, aiming to understand the effect of primary carbides, inclusions, and the metallic matrix on their effective fracture toughness and strength. Microstructurally different steels were investigated. It is found that cracks nucleate on carbides or inclusions at stress values lower than the fracture resistance. It is experimentally evidenced that such cracks exhibit an increasing growth resistance as they progressively extend, i.e., R-curve behavior. Ingot cast steels present a rising R-curve, which implies that the effective toughness developed by small cracks is lower than that determined with long artificial cracks. On the other hand, cracks grow steadily in the powder metallurgy tool steel, yielding as a result a flat R-curve. Accordingly, effective toughness for this material is mostly independent of the crack size. Thus, differences in fracture toughness values measured using short and long cracks must be considered when assessing fracture resistance of tool steels, especially when tool performance is controlled by short cracks. Hence, material selection for tools or development of new steel grades should take into consideration R-curve concepts, in order to avoid unexpected tool failures or to optimize microstructural design of tool steels, respectively.