Notch Tip Plastic Research Articles

Plane Stress Fracture Toughness Testing of Freestanding Ultra-Thin Nanocrystalline Gold Films on Water Surface.

Fracture toughness, which is the resistance of a material to crack propagation, is a critical material property for ensuring the mechanical reliability of damage-tolerant design. Recently, damage-tolerant design is introduced to flexible electronics by adopting micro-cracked ultra-thin nanocrystalline (NC) gold films as stretchable electrodes in a plane stress state. However, experimental investigation of the plane stress fracture toughness of those films remains challenging due to the intrinsic fragility from their sub-100nm thicknesses. Here, a quantitative method for systematically evaluating the plane stress fracture toughness of freestanding ultra-thin NC gold film on water surface platform is presented. After effectively fabricating single-edge-notched-tension samples with femtosecond laser, mode I stress intensity factors are measured in the plane stress state on water surface. Moreover, investigation regarding the effect of notch length, notch sharpness, and notch tip plasticity validates this method based on linear elastic fracture mechanics theory. As a demonstration, the thickness-dependent plane stress fracture toughness of ultra-thin NC gold films is qualitatively unveiled. It is revealed that the thickness confinement effect on grain boundary sliding induces a transition in fracture behavior. This method is expected to further clarify the fracture-related properties of various ultra-thin films for next-generation electronics.

Fracture toughness of a rejuvenated β-Ti reinforced bulk metallic glass matrix composite

• Cryothermal cycling is performed on embrittled bulk metallic glass composite. • Plasticity of BMGC examined using nanoindentation, DSC and compression tests. • Mode I notch toughness of CTC treated BMGC is same as brittle BMGC. • Rejuvenation is hampered by chemical short range ordering of constituents in amorphous matrix. A β-Ti dendrite reinforced Zr-based bulk metallic glass composite (BMGC) was found to be brittle when cast in a large size. The reasons for the embrittlement and the effectiveness of the cryothermal cycling (CTC) treatment in restoring the mode I fracture toughness are examined. Plasticity in all the CTC treated BMGC is estimated from the distribution and occurrence of pop-ins in nanoindentation tests and by measuring the magnitude of enthalpy of relaxation (Δ H rel ) via differential scanning calorimetry (DSC). This is further validated by examining the strain-to-failure ( ε f ) in compression tests. Mode I fracture behaviour of the as-cast embrittled BMGC and the CTC treated BMGC, which exhibits maximum plasticity, is examined. Results show that both BMGCs are equally brittle and exhibit 5 times lower notch toughness ( K QJ ) than their tougher counterpart. Post-facto imaging of the side surfaces reveals the absence of notch-tip plasticity in both BMGCs. The lack of notch tip plasticity of CTC treated BMGC, despite exhibiting signatures of plasticity in nanoindentation and higher Δ H rel is rationalized by reassessing the origin of pop-ins in nanoindentation tests and describing the variations in chemical and topological short range ordering during CTC, respectively. Implications of these results in terms of improving the fracture toughness of structurally relaxed BMGCs via CTC are discussed.

Fracture Behavior of Two Biopolymers Containing Notches: Effects of Notch Tip Plasticity

This paper analyzes the notch effect on the fracture behavior of two biomaterials (a brittle bone cement and a ductile dental material) under mode I loading. U-notched Brazilian disk (UNBD) specimens of both materials were tested under remote compression, determining the corresponding fracture loads and load-displacement curves. Additionally, cracked rectangular and semicircular bend (SCB) specimens were tested under symmetric three-point bending in order to determine the fracture toughness of the two materials. Then, fracture loads were derived theoretically by applying the maximum tangential stress (MTS) and the mean stress (MS) criteria. Due to the brittle linear elastic behavior of the bone cement material, the MTS and MS criteria were directly applied to this material; however, given the significant nonlinear behavior of the dental material, the two fracture criteria were combined with the Equivalent Material Concept (EMC) for the fracture analyses of the dental material specimens. The results reveal a very good accuracy of both the MTS and the MS criteria for the fracture analysis of bone cement notched specimens. In the case of the dental material, very good results are also obtained when combining the MTS and the MS criteria with the EMC. The proposed approach can be useful for the fracture analysis of a wide range of biopolymers, from brittle to ductile behavior.

Notch tip plastic zone determination by extending Irwin’s model

With the aid of some explicit formulas of the elastic stress fields at the neighborhood of U- and blunt V-shaped notches and also using the Tresca and Von-Mises yield criteria, the plastic zone size at the neighborhood of such notches under mode I loading and plane-stress/strain conditions is determined by extending Irwin’s model. Then, for verifying the analytical results, elastic-plastic finite element analyses are done on some notched specimens and the corresponding numerical results are compared with the analytical estimations. It is shown that for the most cases, the effective plastic zone size, which is necessary for determining the type of ductile failure, can be successfully estimated by using the proposed analytical formulas. In addition, due to lack of accuracy of the analytical stress fields used in this study, the shapes of the plastic zones obtained by the analytical and numerical methods are not identical for most cases. It is also revealed that by using the analytical method based on the linear elastic solution instead of the elastic-plastic solutions, which are complicated and time-consuming, the effective plastic zone size at the neighborhood of blunt notches can be determined rapidly and conveniently.

Investigation of Mode I Notch Toughness of Zr41.2Ti13.8Cu10Ni12.5Be22.5 Metallic Glass under Dynamic Loading Conditions

Based on dynamic three-point bending tests, the dynamic notch toughness ( $$ K_{\text{Q}}^{\text{d}} $$ ) of Zr41.2Ti13.8Cu10Ni12.5Be22.5 (Vit 1) bulk metallic glass (BMG) was found to be sensitive to stress intensity factor rate ( $$ \dot{K}_{\text{Q}}^{\text{d}} $$ ), which varied from 5.21 to 31.90 MPa m1/2. The number of shear bands (Ns) in the notch tip plastic zone was quantitatively analyzed. The phenomenon wherein Ns decreased with increasing loading rate was explained based on the theory of the shear transformation zone and the softening mechanism. Then, power law relationships were established among Ns, $$ K_{\text{Q}}^{\text{d}} $$ and $$ \dot{K}_{\text{Q}}^{\text{d}} $$ . The results showed that shear bands can affect $$ K_{\text{Q}}^{\text{d}} $$ and $$ \dot{K}_{\text{Q}}^{\text{d}} $$ and act as a bridge connecting $$ K_{\text{Q}}^{\text{d}} $$ and $$ \dot{K}_{\text{Q}}^{\text{d}} $$ . The sensitivity of $$ K_{\text{Q}}^{\text{d}} $$ to $$ \dot{K}_{\text{Q}}^{\text{d}} $$ in BMGs can be well explained by the variation of Ns with loading rate.

A quantitative connection between shear band mediated plasticity and fracture initiation toughness of metallic glasses

While it is well recognized, albeit qualitatively, that shear band mediated plasticity ahead of crack or notch tips is the raison d'être for the high fracture toughness of 'ductile' bulk metallic glasses (BMGs), quantitative connection between those two material properties is yet to be established. In an attempt to study this, we examine if mode I fracture initiation toughness, KIc, of a number of BMGs can be related to the shear band number, Ni, which is a discretized measure of plasticity in MGs, around spherical indentation impressions that are made to a fracture mechanism based predetermined indentation strain. Results show that KIc scales with (Ni)3/2. Then, the relation between the shear band density in the notch tip plastic zone, Nn, and KIc is examined, which shows that a power law: KIc∝(Nn)1/2, captures the data reported in literature for a number of BMGs. This result confirms that it is indeed the notch tip plasticity that determines KIc of BMGs. The power law exponent of 0.5 is rationalized by recourse to elasto-plastic fracture mechanics. Possible connections between Ni and Nn, ways of enhancing the latter so as to increase KIc, and the central role played by the relative density of MGs in determining both elastic, plastic, and fracture responses are discussed.

Crack initiation and propagation in composite microstructure of dentin

Dentin possesses unique hierarchical structure through long-term natural selection, which imparts exceptional mechanical properties to this hard tissue. In this study, the combined effects of ductile fracture of intertubular dentin (ITD) and brittle cracking of peritubular dentin (PTD) on the crack initiation and propagation in the composite microstructure of dentin are explored. A micromechanical model accounting for the unique two-layer microstructure of dentin is developed and numerical simulations of fracture of microstructured dentin are performed. It is found that microcracking of PTD prior to the penetration of main crack into PTD and crack deflection along the interface between PTD and ITD are two major mechanisms involved in the fracture of microstructured dentin, which is in a good agreement with experimental observations. The competition between the two mechanisms is governed by PTD strength. Furthermore, we reveal that the elastic and fracture properties of PTD and strain hardening of ITD greatly affect the fracture behavior of dentin. The decrease in elastic modulus and increase in tensile strength of PTD elevate the notch tip plasticity, increasing the propensity of crack initiation at notch tip. Whereas such variations in elastic modulus and tensile strength of PTD can lead to the transition of fracture mechanism from multiple void interactions to crack-void interaction, thereby enhancing toughness of dentin. Increasing the strain hardening exponent of ITD can also give rise to the amplified toughness.

Finite element simulation on Cu/CuZr crystalline/amorphous laminate under three point bending test with a stationary notch

In this work, the fracture behavior of crystalline/amorphous laminate under three point bending and the effects of crystalline layers on the notch tip plasticity were studied. For this purpose, finite element simulations under plane strain, small scale yielding conditions were carried out. The numerical simulation results reveal that, the fracture toughness is significantly improved by the laminated composite microstructure when compared to the bulk metallic glasses. Moreover, the fracture toughness will increase with the increasing of the number of crystalline layers. The higher the notch length to specimen width ratio, the worse is the fracture toughness of crystalline/amorphous laminate. This simulation method can also provide a method to design a reasonable structure for required behaviors.

The Effect of Notch Tip Position on the Charpy Impact Energy for Bainitic and Martensitic Functionally Graded Steels

Functionally graded steels (FGS) are a group of functionally graded materials with elastic-plastic properties that are recently produced from austenitic stainless steel and carbon ferritic steel via electroslag remelting process. FGSs provide a possible solution to improve the properties of composites including martensitic and bainitic brittle phases. In the present work, keeping into account the relationship between the impact energy and the notch tip plastic zone size, an analytical model has been developed to predict the Charpy impact energy of bainitic and martensitic FGSs. The Charpy impact energy of the FGSs is compared with that of a specimen made of the homogeneous material corresponding to the layer that includes the notch tip. Moreover, three-dimensional finite element method (FEM) simulation of the process has been carried out via ABAQUS software. The material properties of the layers have been obtained considering the Holloman law for the plastic region. Meanwhile, an exponential variations of the material parameters along the specimen width have been considered. The results of the model show a sound agreement with previous results taken from the literature and the FEM results.

Effect of secondary orientation on notch-tip plasticity in superalloy single crystals

Numerical and experimental evolutions of slip fields in notched Ni-Base Single Crystal superalloy tensile specimens are presented as a function of secondary crystallographic orientation. The numerical predictions based on three-dimensional anisotropic elasticity and crystal plasticity are compared with experimental observations. The results illustrate the strong dependence of the slip patterns and the plastic zone size and shape on the secondary orientation of notches, which can have important consequences on crack initiation. Specific orientations or non-symmetric notch geometries lead to non-symmetric patterns on both sides of the sample. The computations show that strongly different plastic zones are expected in the core of the sample and at free surfaces. The ability of the anisotropic elastic model to anticipate the plastic domains, based on identifying dominant slip systems, is confirmed by the crystal plasticity computations, at low load levels. An important observation is that kink shear banding is a real deformation mode operating at crack tips and notches in high strength nickel-based single crystal superalloys for specific orientations.

The Effect of Notch Processing on Fracture of High-Carbon Steel (C70S6)

The effect of starting notch machining methods on fracture splitting of connecting rod was studied by axial tensile tests with single edge notch. The axial tensile specimens were made of the high carbon microalloyed steel (C70S6) which is now most widely used by the connecting rod of fracture splitting. The single edge notch of axial tensile specimens were respectively machined by laser notch、wire cut electrical discharge and broaching. The notch tip plastic deformation of specimens was compared by the fractography. The experimental results indicate that the specimens with laser notch can be fractured by the smallest axial tensile load which is respectively about 20% and 30% smaller than the fracture load of the specimens by wire cut electrical discharge and broaching. Considering the rich micro-local crack transformation hardened zones around the notch by laser the paper present the equivalent critical stress intensity factor KIcL which can be used to calculate the fracture load with laser notch.

Nonpropagating incipient cracks from sharp notches under fatigue

Growing incipient cracks from sharp notches can stop completely even when the remote applied stress amplitude remains constant. As the crack lengthens, the crack-tip driving force, the stress intensity factor, should increase for a constant remote applied stress, yet, arrest occurs. For this reason, the fatigue stress concentration factor K f differs from the conventional stress concentration factor K t for sharp notches. The arrest has been attributed to increased crack growth resistance as an incipient crack lengthens. The increased resistance has been related to plasticity-induced crack closure, which builds up with crack-wake plasticity during crack growth. In this paper we present a different concept based on our unified approach that considers the existence of two fatigue thresholds rather than one. It is shown that nonpropagation of incipient crack occurs when the total stress intensity factor falls below the long crack growth threshold value in terms of K max. Total stress intensity results from both the remote applied stress and the local internal stress. Even when the remote applied load is constant, the local internal stress can decrease sharply as the incipient crack grows away from the notch tip. Notch-tip plasticity contributes to the changes in the internal stresses. Using extensive data from the literature, it is shown that it is the decreasing crack-tip driving force with length that causes the crack arrest phenomenon. Crack growth under tension–tension, tension–compression, and compression–compression fatigue are all accounted for on the basis of gradient in the internal stresses.

ACOUSTIC EMISSION MONITORING OF FATIGUE DAMAGE IN METALS

The objective of this study was to investigate and develop/adapt acoustic emission (AE) methods for detection and characterization of fatigue damage growth in metals. The materials investigated were 2024-T3 aluminum and 4340 steel. Edge-notch and compact tension specimens were tested under cyclic tensile loading. The investigation consisted of signal/noise discrimination, direct crack growth monitoring, acquisition of acoustic emission data, analysis of AE data and correlation of AE data and damage growth. In the case of aluminum the AE output consists of three characteristic parts corresponding to three stages of crack propagation; the first stage of high but decreasing AE rate, the second stage with a low and nearly constant rate and extending over 80% of the specimen lifetime and the third stage with increasing AE rate up to failure. The rate of AE output in the second stage can be described by a power law in terms of the stress intensity factor range, analogous to the Paris law for crack growth rate. In the case of steel AE results from crack extension, notch tip plasticity and closure, and plasticity dominated rapid crack propagation. The various sources of AE activity were analyzed based on the phase of the loading cycle at which they occur. A high rise in AE activity in the first half of the fatigue life has been attributed to a transition from plane strain to plane stress crack propagation.

Crack tip and notch tip plastic zone size measurement by the laser speckle technique

A laser speckle technique, together with a computer-based image processing system, was used to measure the extent of the elastic-plastic boundary ahead of a static mode 1 crack under small-scale yielding. The technique used a simple optical set-up and did not require surface contact with the specimen. A recently proposed correlation parameter called the Integrated Peak Spectral Intensity H i, was used to correlate the speckle images obtained with the state of strain around a crack tip and the subsequent mapping of the plastic zone. The experimentally obtained plastic zone around a narrow slit obtained by this technique showed reasonable agreement with predictions using Inglis' solution. For a fatigue crack, the extent of the experimental plastic zone ahead of a sharp crack was as expected larger than that predicted by linear elastic fracture mechanics, but agreed well with results corrected for load shedding at the crack tip. The present results indicate that the extent of the elastic-plastic boundary can be measured accurately with the laser speckle technique.

The Effect of Mean Stress on the Fatigue Limit of High Tensile Bolts

Currently engineers use modifications to empirical rules such as the Goodman line or the Gerber parabola, including ideas about notch tip plasticity, to predict the fatigue limit of notched specimens (including bolts) at varying mean stresses. This study compares a large data set obtained from tests on bolts at many different levels of mean stress with these empirical formulations. The data show that the empirical rules are adequate for limited ranges of mean stress. Some new ideas are also presented, which improve the ability of the empirical rules to predict behaviour at high mean stress and for improved design procedures.

Elastoplastic Plane Strain Analysis of Stresses and Strains at the Notch Root

For the evaluation of the local elastoplastic strains and stresses at the notch root suitable approximation formulas of sufficient accuracy are often used. In the present study the “equivalent strain energy density” concept for elastic-plastic notch strain-stress analysis has been developed. It was found that the evaluation of the strain energy density in the notch tip plastic zones does not require any input data other than the material stress-strain relation and the elastic stress concentration factor. The concept was verified on the basis of the results obtained from plane strain elastic-plastic finite element analysis using the material model after Mro´z. Comparison of the two sets of results revealed satisfactory accuracy of the equivalent strain energy concept. It was also shown that all stress and strain components in the notch tip can be calculated by complementing the method with Hencky’s equations. Neuber-based calculations were also included in the study. It was found that the energy concept was superior to Neuber’s rule, especially in the presence of high inelastic strains in the notch tip.

Determination of notch-tip plasticity by X-ray diffraction and comparison to continuum mechanics analysis

Dislocation-free silicon crystals of ({\bar 2 \bar 1 \bar 1}) orientation with a hyperbolic notch, subjected to tensile deformation at 1073 K, were used as model material for the analysis of the induced plastic zone. The results obtained by X-ray topography and X-ray rocking-curve measurements were compared to theoretical calculations and predictions based on continuum mechanics. Good agreement between experiment and theory was obtained regarding the shape of the plastic zone, the contribution of the active slip systems to the size of the plastic zone and the direction of the maximum plastic strain trajectory in the zone. Discrepancies between experiment and theory regarding the symmetry relation of the plastic zone lobes and the dislocation density near the notch tip were attributed to the interactions and resulting work-hardening. These aspects were not taken into account in calculations of continuum mechanics.