R-curve Behavior Research Articles

Exploring the fracture toughness and fatigue crack growth behavior of MoRe alloys

The fracture and fatigue crack growth behavior of two molybdenum alloys, containing 41 wt-% and 47.5 wt-% rhenium, respectively, are investigated. These alloys were provided in form of cold-wrought rods of 6 mm diameter and exhibit a refined microstructure with highly elongated grains and a strong fiber texture. Similarly processed pure molybdenum was used as reference material and exhibits a significantly coarser microstructure. SEN(T) and C(T) specimens were tested with R-L and L-R orientation. In both, quasi-static and fatigue crack growth experiments, L-R oriented cracks immediately kinked by 90° into the direction of grain elongation. This yields fracture toughness values and effective and long crack threshold values about twice as high as for R-L oriented cracks, which is in good agreement with calculations of a reduced local crack driving force. In both MoRe alloys a cyclic R-curve behavior was captured in fatigue crack growth tests at a load ratio of R = 0.1, while for MoRe47.5 it was still present at R = 0.7. This is attributed mainly to the coarser microstructure. The effective thresholds ∆Kth,eff of both MoRe alloys are remarkably low and deviate from a commonly used estimation, especially for the MoRe47.5 material. It is proposed that plasticity in these materials is facilitated by twinning, leading to the emission of partial dislocations from the crack tip. Although no clear microstructural or fractographic evidence was found, a recalculation of ∆Kth,eff considering partial dislocations indicates a good correlation with experimental values.

Mechanism based four-linear cohesive zone model for mode I fracture of different stacking sequence CFRP laminates

Delamination, a prevalent failure mode observed in laminated composites, exerts a significant impact on structural integrity and performance. The occurrence of fiber bridging during the fracture process adds complexity and elevates the research challenges associated with this phenomenon. Existing models exhibit limitations in accurately capturing bridging behavior and discerning its underlying mechanical mechanisms. This study addresses these limitations by analyzing experimental results, employing the J-integral, and analyzing R-curve behavior, proposing a mechanism-based four-linear cohesive zone model along with a new finite element implementation method. Comprising three overlapping bi-linear CZMs, this model effectively simulates mode I fracture behavior in laminates with different stacking sequences. Moreover, it intuitively illustrates the mechanical mechanisms during crack propagation and offers simplicity in implementation. This research contributes to a deeper understanding of composite fracture mechanics and provides a practical model for predicting delamination behavior in laminated structures.

Influence of deformation, microstructure, and temperature on the fracture resistance of technically pure tungsten

The fracture resistance of technically pure W with pre-deformed and recrystallized microstructures was tested in a temperature range of ambient to 700 °C. To account for the impact of microstructure anisotropy, samples with different specimen orientations were investigated. Room temperature tests were carried out in a scanning electron microscope and at elevated temperatures in a vacuum furnace. Both, microstructure and testing temperature significantly influence the fracture resistance of W and a strong dependence of the crack propagation resistance on the crack plane orientation was found. Pre-deformation of the testing material increases the fracture resistance in terms of the crack initiation toughness but shortens the measurable crack resistance curve (R-curve). Testing at elevated temperatures results in higher initiation toughness for both states, pre-deformed and recrystallized; however, only the recrystallized structure shows an R-curve behavior for the used sample geometry.

A fatigue test based on inclined loading block concept to benchmark delamination growth considering loading history and [formula omitted]-curve effect

The main objective of this paper is to present a delamination benchmark test concept for composite materials that develop non-self-similar delamination in characterization specimens. The non-self-similar delamination is induced by rotating the loading blocks. The simplicity of the test allows for analyzing the loading mode history by concatenating different loading conditions, such as static and fatigue loading, under multiple loading modes. The methodology introduced in this paper can be particularized for any given composite material set and any sequence of loading conditions. To demonstrate the capabilities of the benchmark test, a case study is presented using AS4D/PEKK-FC thermoplastic composite material, which exhibits strong R-curve behavior. A sequence of opening and shear failure modes was applied under static and fatigue loading, providing an experimental data set that is ready to be used as a part of the validation of numerical predictive delamination models. The delamination process was monitored by X-ray radiography, and the final fracture surfaces were analyzed with scanning electron microscopy (SEM), giving a physical insight into the contribution of the fracture mechanisms to the delamination process.

Impact of thermal shock on the R-curve and subcritical damage behaviour of flame-sprayed alumina compounds

An alumina rich Al2O3–ZrO2–TiO2 compound was used for the preparation of self-supporting parts via the rod flame spraying technology. The as-sprayed material was compared to self-supporting parts, fabricated from commercially available alumina rods. For both materials, the flexural strength, the fracture resistance, and the behaviour under subcritical loading was evaluated and compared, either before as well as after cold thermal shock. While the flexural strength and the subcritical damaging of both materials were basically affected through thermal shock in a similar manner, the Al2O3–ZrO2–TiO2 compound showed an outstanding behaviour in terms of its fracture resistance, which was only barely reduced after thermal shock quenching.

Sintered reaction-bonded silicon nitride ceramics for power-device substrates -review-

This review addressed the recent progress of sintered reaction‐bonded Si3N4 (SRBSN) ceramics which are expected to be used as ceramic substrates of the next-generation power devices. Following an overview of thermal conductivities of Si3N4 ceramics and their improvement strategies, we described the advantages of the SRBSN routes. Because of the low content of lattice oxygen, the SRBSN ceramics possess significantly high thermal conductivities, compared to Si3N4 ceramics prepared by conventional methods. This material also showed exceptionally high fracture toughness and the strong rising R-curve behavior. The properties of the SRBSN ceramics are largely affected by the nitridation conditions, including the temperature, pressure and heating rate, and the sintering additive ratios. The thermal fatigue tests revealed the excellent thermal fatigue resistance of the SRBSN substrates, compared with those of other ceramic substrates. The strength retention ratio after thermal fatigue was clearly proportional to the fracture toughness. The dielectric breakdown strength (DBS) of the SRBSN ceramics with large fibrous grains showed a thickness dependency reverse to the normal (lower DBS in thinner substrates).

On the strength and fracture toughness of an additive manufactured CrCoNi medium-entropy alloy

An additively manufactured (nominally equiatomic) CrCoNi alloy was processed by laser powder bed fusion (LPBF). At ambient temperatures (298 K), this medium-entropy alloy displayed a yield strength, σy of ∼691 ± 9 MPa, and an ultimate tensile strength, σu of ∼926 ± 15.2 MPa; at cryogenic temperatures (77 K), yield and tensile strengths increased respectively to σy ∼ 944 ± 6 MPa and σu ∼ 1382 ± 11 MPa. These strength levels are 57 and 44% higher than that of the wrought alloy, due to strengthening from the solidification cellular structures intertwined with dislocations in the LPBF CrCoNi. The crack-initiation fracture toughness, KJIc was measured to be ∼183.7 ± 28 MPa√m at 298 K; this value marginally decreased by ∼4% to ∼176 ± 11 MPa√m at 77 K. These KJIc values of the LPBF CrCoNi were 11% and 35% lower than the wrought CrCoNi alloy at 298 K and 77 K, respectively. The resistance to crack growth of the LPBF CrCoNi from its hierarchical micro- and meso‑structures was evaluated using nonlinear-elastic fracture mechanics by measuring R-curve behavior in the form of the J-integral as a function of crack extension. The specific features of the hierarchical microstructures at different length-scales provide a basis for the strengthening and toughening properties of this additively manufactured medium-entropy alloy. This correlation between the deformation and the hierarchical microstructures at different length-scales may provide future guidance for improving the fracture toughness properties of medium-entropy alloys.

Toughening of face-sheet core bonds in sandwich structures

Methods of improving the toughness of the bond between a foam core and a carbon fibre face-sheet in a sandwich structure were investigated. The Single Cantilever Beam (SCB) on a travelling platform was identified as an appropriate mode-I dominant test-method. The introduction of machined grooves in the foam resulted in a 50% improvement in the measured toughness of the face-sheet-core bond. Toughening of the face-sheets via core–shell rubber particles resulted in a change in fracture locus away from the interface and into the foam. The use of aramid fibre-reinforced foam as the core of the sandwich was also found to improve the interface bond toughness by up to 50%. The fibre-reinforced foams promoted the emergence of R-curve behaviour as the crack propagated.

Influence of curing pressure on the mode I static and fatigue delamination growth behavior of CFRP laminates

Curing conditions affect the mechanical properties of manufactured composite structures. However, the effect of curing pressure on the delamination behavior of laminates is still lack of investigation. This work studies the mode I static and fatigue delamination of carbon/epoxy laminates prepared at curing pressures of 1 MPa and 3 MPa. Delamination tests are conducted using double cantilever beam set-up. Test results show that more bridging fibers present in the laminates cured at 3 MPa, with more significant R-curve behavior, higher values of steady-state fracture toughness and maximum bridging stress than those in the laminates cured at 1 MPa. SEM images show that the laminates cured at 3 MPa mainly occur interlaminar damage while the major failure mechanism in the laminates cured at 1 MPa is the fiber/matrix debonding. A normalized model is proposed to describe the fatigue delamination behavior of laminates with fiber bridging effect. It shows that all fatigue data can be characterized by a single linear curve and curing pressure affects the slope of the linear curve. Furthermore, simulation for the delamination growth is conducted based on a tri-linear cohesive zone model. Good agreements between experimental and predicted load–displacement responses are achieved, illustrating the applicability of the established FE model.

Natural mollusk shells as a potential dental material

The mollusk shells in Nature have evolved ingenious architectures and achieved outstanding mechanical properties, thereby demonstrating a potential for tissue engineering applications; nevertheless, despite a broad investigation of them for gaining inspiration towards guiding the design of man-made materials, the mollusk shells have rarely been explored for directly using as a biomedical material. This study offers a preliminary evaluation about the potential and feasibility of natural mollusk shells for using as dental replacements by systematically examining their aesthetic performance, machinability, as well as mechanical and biological properties. The shells exhibit a variety of colors with natural lusters, and can be processed into desired shapes and dimensions with good surface finish. The Strombus latissimus shell has a comparable flexural strength as human teeth, and exhibits higher fracture toughness than most of commercial dental materials along with stable crack extension featured by rising R-curve behavior owing to the effective toughening effects of crossed-lamellar architecture. Additionally, the shell displays a good cytocompatibility and certain antifungal function because of its hydrophilic and negative charged surfaces with low roughness. A simple and viable approach was further exploited for enhancing the hardness of natural mollusk shells by immersing them in aqueous solutions of metal ions. The unique combination of properties makes the natural mollusk shells promising for dental applications which may represent a potentially new protocol for tissue engineering.

Fracture Resistance and Crack Growth Mechanisms in Functionally Graded Ti–TiB

This paper presents the results of fracture tests and crack path observations for a layered functionally graded material (FGM) consisting of Ti and TiB phases. The composition varied in a nearly linear manner from a TiB-rich layer at the bottom to commercially pure (CP) Ti at the top. Elastic properties of the mixed phase interlayers were measured using nanoindentation testing, demonstrating a linear variation with composition. These results differ significantly from approximations calculated in previous studies using a non-linear rule-of-mixtures approach. Fracture tests were conducted on single edge notch bend [SEN(B)] specimens with the notch aligned orthogonal to the direction of the composition gradient. For this crack orientation, "average" R-curve behavior based on the J-integral was investigated to understand the mechanics of crack growth. The value of J was found to be minimal (less than 1 N/mm) below 47 pct volume fraction of TiB compared to a reported value of approximately 150 N/mm for pure Ti. These results indicate that a steeper transition to high concentrations of the metallic phase is necessary to achieve adequate fracture resistance in this metal/ceramic FGM. Observations on the specimen surface indicate crack path toughening mechanisms of this functionally graded material include crack bridging, branching, and deflection.

Determining cohesive parameters in an n-segment constitutive law of interfaces through DCB tests

R-curve behavior usually presents in the delamination growth process of composite laminates, which is mainly results by fiber bridging. To simulate the delamination with R-curve behavior, cohesive zone model with an n-segment constitutive law has been proposed. However, there are many parameters in the constitutive law and it is usually difficult to determine their values. To solve this problem, this study proposes a simple and efficient approach for the determination of an n-segment constitutive law. The determined constitutive law has been implemented in the ABAQUS software, using a user-defined subroutine. Three case studies with different material systems are performed to verify the wide applicability of the proposed approach. Good agreements between experimental and predicted load–displacement responses indicate the robustness of the proposed methodology. Only experimentally recorded load and displacement data are required in this method. This approach has the advantage of being easy to use and no need for parameter adjustment, which makes it convenient for determining any n-segment constitutive law and suitable for practical application.

Highly aligned reduced graphene oxide in alumina composites for strengthening, toughening, and electromagnetic interference shielding

Engineering ceramics with high strength, toughness and electromagnetic interference (EMI) shielding effectiveness (SE) are highly desirable as electromagnetic protecting material in harsh environment. Herein, we show that both excellent mechanical and EMI shielding performance can be realized in alumina composites embedded with highly aligned reduced graphene oxide (RGO), which are readily prepared via sintering of core-shell structured RGO@Al2O3 nanoplates with pressure. Compared to monolithic Al2O3, the highly aligned RGO/Al2O3 composites show simultaneously improved strength and toughness up to ∼26.1% and ∼60.2%, respectively. The steeply rising R-curve behavior proves the better crack tolerance in the highly aligned structure with respect to randomly oriented one. Moreover, the RGO/Al2O3 composites also exhibit a high specific EMI SE reaching ∼34 dB/mm in K band, due to the reflection and highly enhanced absorption after percolation in the out-of-plane direction. These findings provide a novel strategy of designing mechanically reliable engineering ceramic for EMI shielding.

On the static failure behaviour of co-cured composite joints with enhanced interlaminar fracture energies via multiscale toughening

This paper is focused on the multiscale toughened co-cured composite interfaces of carbon/epoxy laminates using vacuum infusion and out-of-autoclave curing—with an emphasis on the role of enhanced interlaminar fracture energies on the static failure of laminate joints. To toughen co-cured interlaminar regions, three toughening routes are used: (i) epoxy matrix toughening with 10 wt% core–shell rubber (CSR) nanoparticles, (ii) 10 g/m2 polyphenylene sulfide (PPS) non-woven micro-fibre veil toughening, and (iii) multiscale toughening by combining epoxy matrix toughening with 10 wt% CSR nanoparticles and 10 g/m2 PPS veils. Double cantilever beam and end-notch flexure tests are conducted with the toughened interfaces for mode-I and mode-II fracture energies. Moreover, three co-cured joint configurations (viz. double-notch single lap, stepped scarf and skin-stiffener joints with the three toughening routes) are tested to characterise the role of enhanced interlaminar fracture energies on the static failure of laminate assemblies. The results show that the three toughening routes have significantly altered the R-curve behaviour and interlaminar fracture energies and that the degree of enhancement in mode-I and mode-II fracture energies is sensitive to the type of toughening route. Based on the material systems tested, the mode-I fracture initiation energy is enhanced by ∼150% with multiscale toughening, ∼65% with particle toughening, and ∼60% with veil toughening; whereas, the mode-II fracture initiation energy is enhanced by ∼85% with veil toughening and ∼35% with multiscale toughening—but reduced by ∼20% with particle toughening. The joint tests show that the toughening routes affect the static failure of the three joint configurations and that the strength and damage evolution of the co-cured joints depend on the interlaminar fracture energies. The strength of the co-cured single lap joints is increased by ∼50% with multiscale toughening and ∼40% with veil toughening; whereas, the strength of the co-cured skin-stiffener joints is enhanced by ∼35% with multiscale toughening and ∼45% with veil toughening. The failure mechanisms observed on the fracture surfaces indicate that the strength/failure behaviour of the co-cured joints depends on the dominant interlaminar fracture mode and the corresponding fracture energies. Overall, it is shown that the multiscale interlaminar toughening routes that are used to address the issue of delamination can also be effectively explored to enhance the static failure of co-cured laminate assemblies by toughening the co-cured interfaces/bondlines.

Effect of Through-the-Thickness Delamination Position on the R-Curve Behavior of Plain-Woven ENF Specimens.

In this study, the effect of through-the-thickness delamination plane position on the R-curve behavior of end-notch-flexure (ENF) specimens was investigated using experimental and numerical procedures. From the experimental point of view, plain-woven E-glass/epoxy ENF specimens with two different delamination planes, i.e., [012//012] and [017//07], were manufactured by hand lay-up method. Afterward, fracture tests were conducted on the specimens by aiding ASTM standards. The main three parameters of R-curves, including the initiation and propagation of mode II interlaminar fracture toughness and the fracture process zone length, were analyzed. The experimental results revealed that changing the delamination position in ENF specimen has a negligible effect on the initiation and steady steady-state toughness values of delamination. In the numerical part, the virtual crack closure technique (VCCT) was used in order to analyze the imitation delamination toughness as well as the contribution of another mode on the obtained delamination toughness. The numerical results indicated that by choosing an appropriate value of cohesive parameters, the trilinear cohesive zone model (CZM) is capable of predicting the initiation as well as propagation of the ENF specimens. Finally, the damage mechanisms at the delaminated interface were investigated with microscopic images taken using a scanning electron microscope.

Crystallized fraction and crystal size effects on the strength and toughness of lithium disilicate glass-ceramics

This work investigated the variation in fracture strength and toughness of stoichiometric lithium disilicate (LS2) glass-ceramics as a function of crystal size (d) and crystallized volume fraction (f), with three average crystal sizes (8, 13 and 34 µm) and a wide range of crystallized fractions (0–100 %). The fracture strength and toughness increased with increasing the crystallized volume fraction. For constant crystallized fraction, KIC increased with crystal size, indicating an R-curve behavior. The mean free path between the crystals limits the maximum size of the critical defect and is the crucial feature controlling fracture strength. Finally, we verified that the contribution to the toughness of R-curve mechanisms in this glass-ceramic is proportional to (f.d)1/2, which agrees with R-curve models for ceramics.

R-curve evaluation of 3YTZP/graphene composites by indirect compliance method

This work addresses the crack growth resistance of 3 mol% Yttria-doped Tetragonal Zirconia Polycrystalline (3YTZP) spark-plasma sintered (SPS) composites containing two types of graphene-based nanomaterials (GBN): exfoliated graphene nanoplatelets (e-GNP) and reduced graphene oxide (rGO). The crack growth resistance of the composites is assessed by means of their R-Curve behavior determined by three-point bending tests on single edge “V” notched beams (SEVNB), in two different orientations of the samples: with the crack path perpendicular or parallel to the pressure axis during the SPS sintering. The sharp edge notches were machined by ultrashort laser pulsed ablation (UPLA). The compliance and optical-based methods for evaluating the crack length are compared on the basis of the experimental R-Curve results in composites with 2.5 vol% rGO tested in the perpendicular orientation. Moreover, the activation of reinforcement mechanisms is evaluated by both the fracture surface inspection by Scanning Electron Microscopy and a compliance analysis. It is shown that the indirect compliance method is relevant and reliable for calculating the R-Curve of 3YTZP/GBN composites. The effect of the type and content of GBN on the crack growth resistance of the composites is also discussed.

R-Curve Behavior of Polyhedral Oligomeric Silsesquioxane (POSS)–Epoxy Nanocomposites

Polyhedral oligomeric silsesquioxane (POSS) is a suitable nanoscale reinforcement for thermosetting polymers, such as epoxy resin systems in order to modify its mechanical, thermal and chemical properties. The inclusion of POSS in the epoxy resin at higher loading (greater than 1 wt.%); however, it introduces the ductility during the fracture behavior of these nanocomposites. Consequently, the J-integral is used to quantify the fracture behavior of these materials and characterize the crack growth resistance curve against stable crack growth. A range of nanocomposites is prepared by adding 0.5, 1, 3, 5, and 8 wt.% of glycidyl POSS into DGEBF epoxy resin cured with an amine-based curing agent. From fracture toughness experiments, the load-displacement result confirms that when the POSS reinforcement is greater than 1 wt.%, the fracture behavior of the nanocomposite changes from brittle to ductile. For both brittle and ductile nanocomposites, the addition of POSS molecules improves the crack initiation toughness. The development of POSS–POSS compliant domains, reported previously, is responsible for this change in the failure behavior. The fractured images of POSS–epoxy nanocomposites, obtained by using scanning electron microscopy, show that the increase in fracture resistance at higher values of POSS loading occurs due to the extensive shear yielding. Meanwhile, the increased fracture toughness at lower values of POSS loading occurs due to crack pinning and crack deflection.

A step toward bio-inspired dental composites

This feasibility study aimed to develop a new composite material of aligned glass flakes in a polymer resin matrix inspired by the biological composite nacre. The experimental composite was processed by an adapted method of pressing a glass flake and resin monomer system. By pressing and allowing the excess monomer to flow out, the long axis of the flakes was aligned. The resultant anisotropic composite with silanized and non-silanized glass flakes were subjected to fracture toughness tests. We observed increasing fracture toughness with increasing crack extension (Δa) known as resistance curve (R-curve) behavior. Silanized specimens had higher stress intensity KR-Δa over non-silanized specimens, whereas non-silanized specimens had a much lower Young’s modulus, and higher nonlinear plastic-elastic JR-Δa R-curve. In comparison with conventional composites, flake-reinforced composites can sustain continued crack growth for more significant extensions. The primary toughening mechanism seen in flake-reinforced composites was crack deviation and crack branching. We produced an anisotropic model of glass flake-reinforced composite showing elevated toughening potential and a prominent R-curve effect. The feasibility of flake reinforcement of dental composites has been shown using a relatively efficient method. The use of a biomimetic, nacre-inspired reinforcement concept might guide further research toward improvement of dental restorative materials.

Fatigue driven delamination in composite structures: Definition and assessment of a novel fracture mechanics based computational tool

The development of numerical methodologies to investigate material damages is a crucial aspect of aerospace components design. The advent of composite materials has made this aspect more critical due to their anisotropic properties, which result in damage mechanisms difficult to control and predict. Despite the progress made in the development of computational approaches for composites failure assessment, fatigue damage remains an open issue. This work deals with the development of a robust and efficient computational tool to simulate the fatigue driven delamination in complex composite structures. The main objective is to exploit the peculiarities, in terms of mesh and load step size independency, of the well-established SMart–time XB procedure, based on the Virtual Crack Closure Technique approach, to develop a Paris Law-based module to mimic the delamination growth rate due to cyclic loads. The implemented fatigue block interacts with the already existing modules, thus simulating the fatigue driven delamination without mesh dependency and potentially accounting for the R-curve behaviour of the material. The procedure takes advantage of the solver of the commercial Finite Element code Ansys Mechanical but is fully implemented in the Ansys Parametric Design Language, resulting in an absolutely versatile and parametric procedure. The promoted numerical tool has been firstly validated at coupon level considering the literature available Single Leg Bending-based benchmark. Then, the post–buckling behaviour of a typical aeronautical stiffened panel, based on a literature experimental test, has been studied under non-constant cyclic load conditions. Comparison against literature numerical and experimental data have proved the efficiency of the proposed computational tool to simulate fatigue-driven delamination both at coupon level and in complex structures.This work deals with the development of a robust and efficient computational tool to simulate the fatigue driven delamination in complex composite structures. The main objective is to exploit mesh and load independency peculiarities of the well-established SMart–time XB procedure, to develop a Paris Law-based module to mimic the delamination growth due to cyclic loads. The procedure is fully implemented in the Ansys Parametric Design Language, resulting in a versatile and parametric procedure. The promoted tool has been firstly validated at coupon level. Then, the post–buckling behaviour of a stiffened panel, based on a literature experimental test, has been investigated.