Notch Root Radius Research Articles

Tensile Notch Sensitivity of Additively Manufactured IN 625 Superalloy

The notch sensitivity of additively manufactured IN 625 superalloy produces by laser powder bed fusion (LPBF) has been investigated by tensile testing of cylindrical test pieces. Smooth and V-notched test pieces with four different radii were tested both in as-built state and after a stress relief heat treatment for 1 h at 900 °C. Regardless of the notch root radius, the investigated alloy exhibits notch strength ratios higher than unity in both as-built and in stress-relieved states, showing that the additive manufactured IN 625 alloy is not prone to brittleness induced by the presence of V-notches. Higher values of notch strength ratios were recorded for the as-built material as a result of the higher internal stress level induced by the manufacturing process. Due to the higher triaxiality of stresses induced by notches, for both as-built and stress-relieved states, the proof strength of the notched test pieces is even higher than the tensile strength of the smooth test pieces tested in the same conditions. SEM fractographic analysis revealed a mixed mode of ductile and brittle fracture morphology of the V-notched specimens regardless the notch root radius. A more dominant ductile mode of fracture was encountered for stress-relieved test pieces than in the case of the as-built state. However, future research is needed to better understand the influence of notches on additive manufactured IN 625 alloy behaviour under more complex stresses.

Numerical investigation of tensile response of notched bulk metallic glass composite specimens

In this work, plane strain finite element and atomistic simulations of tensile response of double edge notched bulk metallic glass composite (BMGC) samples are conducted. A special constitutive model is used to represent the response of the bulk metallic glass matrix along with J 2 flow theory of plasticity to characterize the crystalline dendrites in the former, while a CuZr based glass matrix containing single crystal Cu dendrites is modeled in the latter. It is found that the ratio of notch root radius to the distance between the notch tip and the nearest dendrite, R/l 1, is an important parameter that governs the plastic deformation behavior and possible failure mechanisms. Both finite element and atomistic analyses show that as R/l 1 increases from a small to moderate value, a transition occurs in plastic flow through multiple shear banding with deflection by dendrites to ligament necking. On further increase in the above notch acuity parameter, the deformation behavior again changes to multiple shear banding without much hindrance from dendrites. Specimens with moderately blunt notches (as characterized by the value of R/l 1) having high hardening elongated dendrites exhibit pronounced plastic deformation along the ligament resulting in necking. The influence of BMGC microstructure and hardening of dendrites is also investigated from the finite element analyses.

Simplified approach for ductile fracture mechanics SSTT and its application to Eurofer97

Abstract The determination of fracture-mechanical properties is often very challenging, because the available standards like ASTM E1820 need specific size-requirements for the specimen dimensions to obtain valid fracture toughness. Especially in the ductile regime, where the presence of plasticity around the crack tip is affected by the multiaxial stress state and its triaxiality, the size-requirements are frequently not met. The fulfilment of the size-requirements needs the testing of big specimens, which is often not possible. If we now think of specimens, which are irradiated in test modules for future fusion reactors, their size cannot be as big as required, because the available volume for irradiation is restricted. This fact highlights the need of Small Specimens Test Techniques (SSTT) for the determination of fracture-mechanical properties in the ductile regime. The presented work focuses on an approach for the determination of fracture-mechanical properties in the ductile regime including stable crack growth and crack-resistance behavior. The authors have developed the initial approach some years ago and within this work the approach was simplified as much as possible. The basic idea of the approach is, that the crack growth can be simulated using Finite Element Method combined with a cohesive zone model. The cohesive zone model is a two parametric model, namely the cohesive stress σ c and the cohesive energy Γ c , which are identified on small specimens only. The new simplified approach was now validated on ferritic-martensitic steel Eurofer97 at room temperature. In the past, the approach used complicated features like a CCD camera system and has now been simplified in a way that no CCD camera system is required. The main part of the approach is the identification of cohesive zone parameters (cohesive stress σ c and energy Γ c ) on small specimens. The cohesive stress σ c can be determined on notched round tensile specimens with different notch root radius to account for different stress states or stress triaxialities in the specimen. With dedicated Finite Element modelling a local fracture stress dependent on stress triaxiality can be identified. The cohesive energy Γ c can be carried out by simulating the small fracture-mechanical specimen using the Finite Element Method combined with the cohesive zone model and parameter fitting to experimental results. The cohesive energy Γ c is treated to be identified, if the simulated crack-resistance curve describes the experimental behavior. After identification of these parameters, a big fracture-mechanical specimen can be simulated using the cohesive zone parameters already determined on small specimens. Finally, the crack-resistance curve of a big specimen can be predicted and a valid fracture toughness can be identified if the size-requirements of the big specimens are met. In case the requirements are not fulfilled, a bigger specimen geometry can be simulated until all size criteria are met. With this method, the testing of big specimens can be avoided. For the future there is a Round Robin exercise planned including defined test matrices to demonstrate the general applicability of the approach.

Experimental verification of the virtual isotropic material concept for the last-ply-failure of U-notched quasi-isotropic E-glass/epoxy composite laminates under tension-shear loading

Fracture investigation of U-notched E-glass/epoxy laminated composite specimens with various notch root radii is performed under mixed mode I/II loading conditions both experimentally and theoretically. Rectangular E-glass/epoxy composite laminates with two numbers of ply (8-ply and 16-ply) and the quasi-isotropic [0/90/+45/–45]s lay-up configuration are fabricated for conducting the fracture tests. To measure the damage initiation angles (DIAs) and the last-ply-failure (LPF) loads of the fabricated composite samples containing horizontal and inclined U-notches, as the main aim of this study, the specimens are loaded under tension by the universal testing machine. The experimental LPF loads are theoretically predicted with the aid of a novel concept, called the Virtual Isotropic Material Concept (VIMC). The proposed VIMC is linked to the two well-known stress-based fracture criteria, namely the maximum tangential stress (MTS) and the mean stress (MS) criteria, in the context of the linear elastic notch fracture mechanics (LENFM). It is proved that the two combined criteria, namely the VIMC-MTS and VIMC-MS criteria, can predict well the LPF loads of the U-notched laminated composite specimens tested under mixed mode I/II loading conditions. One of the important merits of these new criteria is that the predictions of the LPF loads of the U-notched composite specimens are performed without complicated and time-wasting ply-by-ply damage analyses.

The influence of fibre alignment on the fracture toughness of anisotropic soft tissue

Finite element (FE) simulations are performed to investigate the effect of fiber induced anisotropy on the notch behavior in hyperelastic skin type materials. The modified anisotropic (MA) model is used to define the constitutive behavior in FE simulations through Abaqus user defined material model UMAT. A parametric study is carried out to examine the effect of fiber orientation, notch root radius and sample geometry on the stress field ahead of the notch tip. A non-dimensional parameter ξ is defined to characterize the combined effect of J energy and average anisotropic energy ϕaniso-avg on the notch behavior. It is shown that fibre orientation significantly influences the stress state and J-integral at the notch. The findings of the present study will be helpful in determining optimal constitution and orientation of skin grafts at locations of high stress and complex geometries, such as corner of eyes and lips, etc.

Analysis of fracture data from notched specimens can provide information on multiscale toughening mechanisms

The identification and quantification of toughening mechanisms in materials is a difficult task which is often made more difficult by the presence of several mechanisms operating at different scales. The hypothesis behind the present work was that the length scales at which these mechanisms operate might be deduced by analysing data from fracture tests conducted on samples containing notches of different root radii. A two stage approach was adopted. Firstly, theoretical models were created using imaginary model materials with well-known toughening mechanisms. In those models having toughening mechanisms on two different scales (known as Dual materials) it was found that the larger-scale mechanism controlled the measured fracture toughness (Kcm) for cracks and sharp notches, whilst the smaller-scale mechanism controlled the behaviour of blunter notches. This change in control created a distinct “kink” in the curve of Kcm as a function of notch root radius. Secondly, experimental data from the literature were examined. Similar kinks were found to be present in the results for some materials, implying Dual behaviour. A method of prediction known as the Theory of Critical Distances (TCD) was applied to the data to estimate the relevant length scales, which in some cases coincided with those of well-known toughening mechanisms. This type of analysis may prove useful for identifying the scale, and relative importance, of toughening mechanisms in a wide variety of materials. It also provides a more accurate way to use the TCD approach to predict the effect of cracks and notches when more than one toughening mechanism is present.

Probabilistic Surface Layer Fatigue Strength Assessment of EN AC-46200 Sand Castings

The local fatigue strength within the aluminium cast surface layer is affected strongly by surface layer porosity and cast surface texture based notches. This article perpetuates the scientific methodology of a previously published fatigue assessment model of sand cast aluminium surface layers in T6 heat treatment condition. A new sampling position with significantly different surface roughness is investigated and the model exponents a 1 and a 2 are re-parametrised to be suited for a significantly increased range of surface roughness values. Furthermore, the fatigue assessment model of specimens in hot isostatic pressing (HIP) heat treatment condition is studied for all sampling positions. The obtained long life fatigue strength results are approximately 6% to 9% conservative, thus proven valid within an range of 30 µm ≤ S v ≤ 260 µm notch valley depth. To enhance engineering feasibility even further, the local concept is extended by a probabilistic approach invoking extreme value statistics. A bivariate distribution enables an advanced probabilistic long life fatigue strength of cast surface textures, based on statistically derived parameters such as extremal valley depth S v i and equivalent notch root radius ρ ¯ i . Summing up, a statistically driven fatigue strength assessment tool of sand cast aluminium surfaces has been developed and features an engineering friendly design method.

On the sensitivity of fracture mechanism to stress concentration configuration in a two-step quenching and partitioning steel

The effect of stress concentration geometry on the fracture behavior and fracture mechanisms of a two-step quenching and partitioning steel consisting of tempered martensite and retained austenite (RA) is investigated using double edge notched tension (DENT) specimens with different notch root radii. The initial notch opening is varied from a fatigue pre-crack to 15 mm radius. The fracture surface consists in flat triangular regions and slant zones. The fracture mode evolves from intergranular brittle fracture to ductile fracture with dimples. The ductile fracture process further changes from internal necking coalescence to a void sheet shear type coalescence when increasing the notch root radius. A similar transition of the fracture behavior is observed along the ligament of the DENT specimen. This change in the fracture mode results from a decrease of the stress triaxiality. The essential work of fracture is equal to $$40\hbox { kJ/m}^{{2}}$$. This is small when looking at the large value of the product of ultimate tensile strength and total elongation ($$\sim 25, 000\, \hbox {MPa}{\cdot }$$%). The small fracture toughness is ascribed to an intergranular fracture mode, which results from the distribution of blocky RA islands along the boundaries of martensitic packets and from the large stress concentration near the notch tip. A proper control of both the amount and morphology of RA during microstructure design is thus essential to generate the best compromise between tensile properties and fracture toughness, and to avoid the relatively low toughness and more brittle failure observed when stress triaxiality increases.

Notch radius effect on fracture toughness of ceramics pertinent to grain size

Unlike fracture toughness, the notch fracture toughness of a ceramic is not a constant; rather, it increases with the notch-root radius ρ in a notched specimen. In this study, by analyzing the fracture measurements of eight different notched ceramics with an average grain size G of 3–40 μm, a simple model describing the relation between the notch fracture toughness and fracture toughness is proposed as a function of the relative notch-root radius ρ/G. The normal distribution is incorporated to consider the inevitable scatter in measurements where fracture mechanisms and errors are present. The results demonstrate that the model can effectively predict the quasi-brittle fracture variation trend for ceramics, including the upper and lower bounds, with 96% reliability, from a normal distribution; thus, it can address virtually all of the experimental data. We also determined that the notch fracture toughness approximates the fracture toughness if ρ ≤ G.

Effect of Triaxial State of Stress on Tensile Behavior of Modified 9Cr-1Mo Steel

In this investigation, effect of triaxial state of stress on tensile behavior of modified 9Cr-1Mo steel has been studied. In order to introduce different triaxial states of stresses, circumferential notches of different notch root radii were incorporated in the smooth specimens. The tensile tests were conducted at room temperature and at a strain rate of 3 × 10−4 s−1 in air environment. The tensile strength increased, and the ductility (% reduction in area) decreased with a decrease in notch root radius. The curve fitting of tensile data of smooth specimen was carried out using various constitutive equations. The Voce constitutive equation was found to represent the tensile data of the smooth specimen up to the point of necking. An approach consisting of Voce equation for pre-necking and an exponential equation for post-necking behavior of the material was used as input material model which could predict the complete tensile response of the material. The tensile data obtained from the analysis were used as input for the estimation of tensile response of the notched specimens. The load–displacement curves of the notched specimens could be predicted well using finite element analysis. The comparison of stress and strain obtained from finite element analysis was also carried out with the Bridgman equations for the notched specimens. Significant difference in stress distribution was observed as compared to the distribution obtained by finite element analysis for relatively sharper notches.

Void growth measurement and modelling in a thermosetting epoxy resin using SEM and tomography techniques

Void growth and failure in an epoxy resin is investigated. Tensile tests are carried out on double-notched round bars. Stress triaxiality in the net section is controlled by the use of two different notch root radii. SEM and computed tomography observations are conducted on regions of interest to identify voids and evaluate their growth. Failure initiation sites are analysed, revealing critical defects in the form of voids or particles. The macroscopic and microscopic experimental results are used to optimize the Gurson–Tvergaard–Needleman model. A finite element analysis is performed to study the mechanical response of the notched specimens. The peaks of the maximum principal stress are found to coincide with the locations of the failure initiation sites observed experimentally, and the model is shown to be able to handle non-uniform initial void distributions.

Fracture loads for blunt notches under mode I loading

In the present study, fracture load evaluation technique for blunt notches under mode I loading is investigated using the mean stress based line criterion. Considering the effect of notch root radius ρ, a new fracture evaluation method, applicable not only for the V-shaped notches but also for other notches such as shallow notches, is developed, For a large notch root radius ρ (i.e. ρ>ρ|Cri-1), the notch fracture can be evaluated by a simple rule that the fracture occurs when the maximum stress σmax reaches the material ultimate tensile strength σC. If ρ is large adequately such that ρ|Cri-1>ρ>ρ|Cri-2, the notch fracture is evaluated as the fracture problem of a circle hole in an infinite plate. Here, ρ|Cri-1 and ρ|Cri-2 are the critical values for ρ to satisfy the σmax-alone condition and the ρ-alone condition, respectively. Moreover, as long as the V-notch condition is fulfilled by the notch geometry, the notch fracture under mode I loading can be treated as the fracture problem of V-shaped notches and evaluated by the generalized notch stress intensity factorKIV,R or the maximum stress at the notch root σmax. Whether the σmax-alone condition, the ρ-alone condition or the V-notch condition is fulfilled is mainly determined by the ratio of the characteristic length d0m to the geometric size of notched specimen.

Building the Kitagawa-Takahashi diagram of flawed materials and components using an optimized V-notched cylindrical specimen

The present technical note illustrates a novel procedure for building the Kitagawa-Takahashi diagram of a flawed material and of notched components made of the same material. The novelty of the method over the existing technical literature is the use of a rounded V-notched cylindrical specimen, whose geometry was optimized to maximize the intensity of the asymptotical notch stress term. In this way, the sensitivity to experimental uncertainties is reduced and no cumbersome fracture mechanics tests are requested to determine the crack threshold of the defect free of the defect-free material counterpart. The only experimental input are the high-cycle fatigue strength and the mean size of the critical defect at the notch tip of three specimen batches differing in the size of the critical defect and/or in the notch root radius. The potentiality of the method is checked for an additively manufactured Ti-6Al-4V alloy.

Fatigue damage evolution and finite element simulation of the samples under different notch morphology

Based on the theory of continuous damage mechanics and the principle of irreversible thermodynamics, the damage evolution model of low cycle fatigue is investigated. By programming the damage evolution model as UMAT subroutine in ABAQUS, the fatigue damage and crack initiation life of notch materials under specific loads are simulated, and the crack initiation location is determined. Furthermore, the effects of root radius, depth and opening angle on crack initiation life are investigated. The results show that the crack initiation occurs easily in the notch root where the damage is the most serious and the plastic strain accumulates fastest under cyclic loading. With the increase of notch depth and root radius, the crack initiation life decreases. For V-notched specimens, when the notch depth remains unchanged, the crack initiation life will decrease with the increase of the opening angle.

Effect of small defects on the fatigue strength of martensitic stainless steels

The defect tolerance of three different martensitic stainless steels (17-4PH, X20Cr13 and AISI403) under cyclic loading was investigated. Fatigue tests were performed with specimens containing diverse artificial defects (corrosion pits, single and multiple drilled holes, sharp circumferential notches and pre-cracked holes). The measured cyclic strengths are compared to predictions based on the area parameter model proposed by Murakami and Endo. This model is well applicable to small sharp defects if the threshold condition for crack propagation determines the fatigue limit. The transition size from small to large defects, areatrans, – above which the threshold stress intensity factor range, ΔKth, becomes a constant value – is between 80 and 166 µm for the investigated steels. For larger defects, the threshold for long cracks, ΔKth,lc, serves well to predict the fatigue strength under fully reversed loading, i.e. at a load ratio of R = −1. Comprehensive tests were performed to study the influence of mean stress, and threshold conditions were determined that enable to predict the fatigue limit at different load ratios.A simple equation is introduced to estimate the critical defect size, areacritical, which is the size above which defects become detrimental under cyclic loading. It has been found that areacritical increases with increasing load ratio while areatrans is independent of R. Furthermore, higher values of the threshold stress intensity factor range were determined for large defects (with sizes larger than areatrans) compared to long cracks if the load ratio is higher than R = −1. This could be explained by the plane stress condition at the material surface which is prevalent for surface defects, while the condition for long cracks can be assumed as plane strain.It is further demonstrated that the effect of small defects on the fatigue strength of stainless steels is highly sensitive to the notch root radius, ρ. Small holes with diameters of 100 µm (ρ = 50 µm) or larger are less detrimental for the fatigue strength than defects with high stress concentrations – such as corrosion pits.

Notch Tensile Behavior of the Mg-Zn-Gd-Zr Alloy

The Mg-Zn-Gd-Zr alloy is one of the important aerospace alloys in the aircraft gearbox applications. The complex geometry of the gearbox introduces several stress concentration points with various intensities. These regions are susceptible to catastrophic failure under mixed loading condition. Therefore, it is important to understand the deformation and failure mode of this alloy for various plastic constraint conditions. In the present work, Mg-4%Zn-1.5%Gd-0.5%Zr alloys were prepared with four different increasing notch root radii (1, 2, 4 and 8 mm). These samples were tested for tensile properties and compared with the smooth condition. In addition, notch sensitivity was determined analytically. The microstructure and fracture samples of the alloy were characterized with the aid of an optical/scanning electron microscope. Tensile test results show that the alloy is notch sensitive and shows notch-strengthening effects. The notch strength ratio increases with the decrease in the notch root radius due to the strong plastic constraint. The predicted and experimental results of the fracture strain with the notch root radius are in qualitative agreement. The void growth rate prediction is qualitatively in agreement with the tensile and fractography results and suggests that the notch geometry has a significant influence on the plastic strain of the alloy. The microstructure of the alloy has equiaxed grains of 74 ± 24 µm with the grain boundary eutectic. The eutectic is composed of Gd-rich Mg phase. The fracture surface has a distinct change from mixed mode to complete cleavage with the increasing notch root radius. The fractography results show that the fracture mode is predominantly intergranular for all the cases.

Mode I Generalised Stress Intensity Factors for rounded notches in orthotropic plates

In this paper, taking advantage of a recent analytical solution for the stress fields in notched orthotropic plates under tension, new equations are provided for the mode I Generalised Stress Intensity Factor (GSIF) in the case of rounded notches. Such equations explicitly consider the role played by the material properties and the notch opening angle, and inherently quantify the stress redistribution due to the finite value of the root radius with respect to the pointed notch case. The main features of the GSIFs when applied to rounded notches are discussed, as well as the combined effect of the notch root radius and the elastic properties of the material.The developed new equations are then used to provide an engineering formula to assess the stress concentration factor of orthotropic plates with notches.Eventually, a GSIF-based fracture criterion is proposed for notched orthotropic plates under mode I, and its validity is discussed against some experimental data on notched composite laminates taken from the literature.

The Relationship between Strength and Toughness in Tempered Steel: Trade‐Off or Invariable?

Two different types of strength‐toughness relations are investigated in tempered steel (tempered at 25–420 °C). It is found that there is a trade‐off relation between strength‐fracture toughness and becomes invariable relation between strength‐impact toughness. The effect of microstructure on the materials toughness is related to the manner of energy consumption, which should be attributed to the notch root radius of the specimen. The coarse carbides and dislocation density inside the martensite lath have distinct effects on the energy for crack initiation (impact toughness) and crack growth (fracture toughness). Additionally, the mechanism of coarse carbides on the tempered martensite embrittlement is elaborated deeply.

Fracture behaviour of p-Aramid and ultra high molecular weight polyethylene based hybrid composite

Damage in the form of delamination and debonding are the most common failure modes observed in polymeric composites used for high end structural applications. The principal aim of this work is to investigate the fracture behaviour of Ultra High Molecular Weight Polyethylene (UHMWPE) and p-aramid based hybrid composite. In this work, an optimized processing condition based on highest flexural strength has been evaluated using Box-Behken design of experiment method to fabricate the hybrid composite. Based on most optimized processing conditions process variable such as 14.2 MPa for pressure, 120 oC for temperature and 12.7 minutes for time, compression moulded hybrid composites were prepared and the same were studied in detail for their interlaminar fracture toughness. In the present study, a finite notch radius that varied from 110 – 750 µm has been employed. The fracture toughness/resistance (K1c) of the material has been evaluated and analyzed by investigating the influence of varying notch root radii. The results obtained from the analysis showed that the critical notch root radius of the hybrid composite is around 340 µm. The load displacement data of three point bend test with varied crack length are used to evaluate plain strain fracture toughness (K1c). The K1c has been found 1.5 MPa√m for the KQ values derived from specimens with a/W of 0.45-0.55.

A Finite Element Analysis for Evaluation of J-Integral in Plates Made of Functionally Graded Materials with a Semicircular Notch

This work introduces a numerical investigation using finite element method to evaluate the J-integral at crack tip in titanium boride (TiB)–titanium (Ti) ceramic–metal functionally graded materials plate with a semicircular notch at side subjected to different mechanical load conditions (mode I and mixed mode). Young’s modulus of the functionally graded material plate varies along the specimen width (notch radius direction r-FGM) with power-law and exponential-law functions. Further, the Poisson’s ratio is taken as a constant in normal direction to the hole with a power-law function. The relation of J-integral with functionally graded material plate parameters (i.e., power-law index, thickness of plate) and geometrical parameters (i.e., normalized crack length, notch radius ratio) is highlighted; these parameters must be optimized in order to improve the performance. The obtained results show that it requires estimating the length of the crack, the plate thickness, the notch root radius, the variation in the material properties of the FGM plate constituents and the crack direction that they have a significant influence on the J-integral at the crack tip, and the controlled it can be significantly reduce the J-integral. It is noticed also that in the mixed mode the J-integral is more affected than in mode I.