Plastic Crack Research Articles

Properties of Rubberized Concrete Prepared from Different Cement Types

At present, global waste tire generation considerably exceeds consumption. Moreover, waste rubber tires (WRTs) are a cause of concern, as huge volumes are being discarded and buried, thus causing serious environmental pollution. Rubberized waste concrete (RWC) is a type of environmentally friendly construction material. The main challenge encountered when manufacturing rubberized concrete is the low adhesive properties between the cement paste and rubber particles. This paper demonstrates the effects, through experiments, of using waste tire rubber instead of recycled coarse aggregate (RCA) on two types of cement, i.e., sulfate-resistant cement (SRC) and ordinary Portland cement (OPC), where SRC is a specially blended cement designed to improve concrete performance and workability in the most aggressive environments. All tested samples contained 10% silica fume (SF) and 0.2% fly ash (FA), and the substitution of recycled aggregate content with waste rubber tier (WRT) at different percentages of 100%, 75%, and 50% was evaluated. The research investigated the synergistic effect on the workability and mechanical properties of various cement types with different amounts of rubber aggregate. It was found that the sulfate-resistant (SRC) type can increase the compressive strength than OPC with a percentage of 25% with the same content of WRT at concrete mix. Moreover, ductility and cracking behavior are improved, and it appears that it is also possible to make lightweight rubber aggregate concrete with this type of mixture.. Using this type of cement, it is possible to restore satisfactory ductility to the waste tires, thus facilitating a reduction in the formation of potential plastic cracks. Moreover, the indicative compressive strength development for SRC with recycled rubber in concrete positively contributes to a reduction in formed cracks. However, SEM microstructural analyses suggest a higher proportion of C–S–H intermixed with sulfate reaction phases of SRC rubberized mortar than those of OPC; thus, given that crystal growth results in a decreased percentage of air voids rather than decreased internal cracking, it is clearly shown that the average crack width increases in OPC mortar compared with SRC. Finally, t-testing was used as an inferential statistical tool to determine whether there is a sizeable distinction between the properties of the two categories of materials, OPC and SRC, by comparing the mean and standard deviation of the values for compressive and tensile strength.

Crack Closure in Cycles with Dwell Times at High Temperature

The growth of short cracks in round bar specimens with a circumferential notch has been investigated by an extensive experimental study. This specific specimen geometry has been applied to determine notch support based on a reduced crack growth rate due to the induced stress gradient compared to situations without a notch. At the same time, this investigation of crack growth in low cycle creep-fatigue conditions reveals a significant influence of dwell times on crack closure, which is discussed in detail in this paper. Therefore, a fracture mechanical approach based on an elastic-(visco)plastic crack growth simulation is used to compute the cyclic effective fatigue and creep crack tip loading. The crack growth rates are then determined by a Paris and Nikbin–Smith–Webster model. All investigations are based on strain controlled conditions at different loading levels. The shape of the applied cycles is trapezoidal, having a dwell time of three minutes at maximum and minimum load, and is symmetric in tension and compression. It turns out that a separate consideration of crack opening and closure reveals an important difference in effective crack tip loading range and therefore has a significant impact on fatigue crack growth. Moreover, this paper shows that the effect of dwell times is linked to the influence on plasticity induced crack closure and to the stress relaxation during the dwell time in compression, yielding less crack closure.

RETRACTED ARTICLE: Research on Construction Risks and Countermeasures of Concrete Dam

The harsh environment will reduce the interlayer bonding quality of mass concrete and cause plastic cracking. These defects will seriously affect the safety and durability of the structure. This study tested the layer state (water content and penetration resistance), interlayer mechanical properties, and early-age crack resistance of concrete to evaluate the impact of extreme weather on concrete interlayer properties and crack resistance. Furthermore, the interlayer splitting tensile strength of concrete under different treatment measures (covering insulation quilts and artificial grooves) was analyzed to find a method to reduce the construction risk of mass concrete. At the same time, the early-age crack resistance of concrete under different treatment measures (covering insulation quilts and adding PVA fibers) was evaluated. The results showed that the interlayer splitting tensile strength of concrete decreased by 50%, 40%, 29%, and 70%, respectively, compared with bulk concrete under extreme weather conditions (high temperature, strong winds, steep descent in temperature, and short-time heavy rainfall). Covering insulation quilts can reduce the construction risk of concrete under extreme weather conditions such as high temperature, strong winds and steep descent in temperature. This is mainly due to the fact that insulation quilt reduces the impact of the external environment on the concrete and effectively prevents the evaporation of moisture inside the concrete. In addition, covering insulation quilts can reduce the total cracking area of concrete under extreme weather conditions (strong winds and dry-heat, strong winds and cold waves, and short-time heavy rainfall) by 85–100%. At the same time, adding PVA fibers can inhibit the generation and expansion of micro-cracks on the concrete surface. This is due to the bridging and cracking resistance of PVA fibers.

Flexural mechanism and design method of novel precast concrete slabs with crossed bent-up rebar

Precast concrete slabs are one of the most widely used types of structural member in building industrialization. In this paper, a novel precast concrete slab with crossed bent-up rebar was proposed, where the rebar of precast concrete units was bent-up and embedded crossways in cast-in-place concrete toppings, forming a novel joint configuration of precast concrete slabs. The effects of two bent-up angles of the rebar in the precast concrete units, different thicknesses of the cast-in-place concrete toppings, and different reinforcement ratios on the failure modes of novel precast concrete slabs were studied using flexural loading tests with eight specimens. The failure modes of the specimens changed from the joint failure to the failure of the termination section of lap-splice rebar (TSLSR), when the horizontal angle of the bent-up rebar changed from 90 to 60°. Bent-up ends with an angle of 60° prevented the joint failure of the novel precast concrete slabs, and strengthened the flexural performance of the joint. The horizontal component force of the bent-up ends markedly strengthened the flexural capacity of the joint, and the vertical component force of the bent-up ends made the precast concrete units connect tightly with the cast-in-place concrete toppings, enhancing the anchorage effectiveness of the lap-splice rebar. There were two primary failure modes of the specimens: joint cracking caused by the yield of the lap-splice rebar in the joint, and plastic cracking failure of the section beyond the TSLSR. Finally, the design equations of the flexural capacity of the joint and the anchorage length of the bent-up ends were established, and the design process of the novel precast concrete slabs was given.

Plastic cracking behaviour of concrete and its interdependence on rheo-physical properties

The major processes that influence and constitute the plastic cracking behaviour of concrete include bleeding, evaporation, settlement, shrinkage, and capillary pressure. These underlying processes mainly occur during the plastic phase of concrete, during which time concrete has considerable rheological properties. Potentially, there should be interactions between these phenomena. The goal of this experimental study is in two phases – showcase the plastic cracking behaviour of concrete and reveal the nature of its interactions with the rheological properties. A background to the envisaged role of rheology is provided, the plastic cracking and rheological behaviours of five concrete mixes were independently investigated, and the relationship between them established. Emphases are placed on the cracking underlying process (settlement, shrinkage, capillary pressure) and the initial/evolving rheo-physical parameters. The plastic cracking behaviour is shown to have three unique stages observable on the plastic cracking behaviour plot. The settlement process is responsible for the interconnectivity with rheology and is interwoven with the plastic shrinkage and capillary pressure. Hence, the rheological interdependence is mainly valid during the settlement period. An initial settlement period is directly linked to the permeability properties while the later period is inversely influenced by the yield stress and its evolution (structuration). The plastic shrinkage and capillary pressure build-up are directly linked to the yield stress and thixotropy. The study suggests that the stiffness evolution of concrete and its suspending mortar in terms of storage modulus does not influence the plastic cracking underlying processes.

Similar experimental study on retaining waterproof coal pillar in composite strata mining

Numerous field examples of coal seam mining show that when coal seams under confined water are mined close to faults, water inrush effects on complex mining surfaces occur. Obeying similarity rules, physical similarity models consisting of sand, lime, and plaster were used to investigate the water conducting process, along with stress and displacement measured by a combination of mechanical senor, total station, and video camera-. Comparing the physical model tests with the calculation results of elastoplastic limit equilibrium theory, the rationality of the model has been verified. Besides, a safe width of the waterproof coal pillar has been obtained. It can be demonstrated from the model observations that the coal seam in front of the mining can be divided into three areas with different characteristics of stress and displacement, namely, which are the fault-affected area, the elastic area, and the plastic yield crack area. A closed-loop water inlet and outlet pipeline composed of a water control platform that can provide stable water pressure, and water bags pre-buried in the fault was used to simulate the water conduction in the fracture zone. Integrate the development law of stress, displacement, and water conduction coming from the upper and lower walls of the fault to further determine the reasonable width of the waterproof coal pillar.

Plastic shrinkage cracking properties of high-performance shotcrete with supplementary cementitious materials

This article examines the characteristics of shotcrete from the standpoint of resistance to plastic shrinkage cracking. The effects of 2%, 3%, and 4% replacement with colloidal silica (CS) with a 10-nm particle size on the performance of shotcrete was examined, as were the effects of addition of supplementary cement materials in combination with CS, such as silica fume (SF) and ultra-fine fly ash (UFFA). Plastic cracking was examined from three perspectives: its effect on strength development (especially at the initial stage), assessment of plastic shrinkage in accordance with the ASTM C1579, and related issues of bleeding and evaporation. Compressive and flexural strength tests were conducted to gain an understanding of the processes involved, and the Intelligent Crack Viewer FCV-30 was used to estimate crack widths. The results show that the replacement with CS increases the compressive and flexural strength during hardening, which increases its resistance to tensile shrinkage stresses. The practical assessment of cracks showed that a significant reduction in the width of plastic shrinkage cracks was also achieved. The combination of 4% SF and 2% CS significantly reduced the risk of cracking and improved strength characteristics. The application of CS reduced the effect of 20% UFFA on plastic cracking.

Preparation of sodium silicate/red mud-based ZSM-5 with glucose as a second template for catalytic cracking of waste plastics into useful chemicals.

ZSM-5 was economically synthesized with red mud (RM) and industrial sodium silicate (ISS) in a tetrapropylammonium bromide (TPABr)–glucose dual-template system. The roles of glucose, Fe and Ca in RM on the formation of ZSM-5 were investigated. The catalytic performances of the resultant ZSM-5 were tested by cracking waste plastics. It was found that the formation of ZSM-5 was attributed to a synergistic effect between TPABr and glucose. The addition of glucose decreased the pH value in the crystallization solution and thus promoted the crystallization effect. Glucose acted as a hard template to generate mesopores. Fe atoms were partly distributed in the framework and partly adsorbed in the pores of ZSM-5, and helped to generate more Lewis acid sites. Ca atoms were mainly adsorbed in the pores of ZSM-5, and showed an inhibitory effect on the formation of zeolites. The synthesized ZSM-5 showed a weakly acidic and mesoporous structure and achieved an enhanced effect on producing gaseous products (gas yield: 85.3%), especially light olefins (C Created by potrace 1.16, written by Peter Selinger 2001-2019 ]]> 2–4) (selectivity: 77.1%) from cracking of low density polyethylene at 500 °C. The long-term cracking experiment showed that the synthesized ZSM-5 is superior in converting waste plastics to light olefins (ethylene and propene) than the commercial ZSM-5.

The influence of temperature on the cracking of plastic concrete

High early age concrete temperatures can lead to many problems such as an increased rate of cement hydration, as well as an increased rate of moisture loss from fresh concrete which can ultimately lead to the occurrence of plastic shrinkage cracking. Concrete is also batched and cast at various ambient temperatures which greatly influences the temperature development of the concrete after placement. There is a need to understand the influence of concrete temperature on the plastic cracking of concrete. This study investigated the temperature development over the thickness of a concrete slab when exposed to different initial concrete and ambient temperatures as well as the effect these factors have on plastic shrinkage cracking. This was achieved by experiments on concrete samples at varying temperatures while measuring the concrete temperature, pore water evaporation, shrinkage, settlement, setting times and plastic shrinkage cracking magnitude. These tests were conducted in a climate controlled chamber. It was concluded that exposure to higher initial concrete and ambient temperatures significantly increases the average temperature over the thickness of the concrete. The evaporation of pore water was higher when exposed to higher evaporation conditions. The plastic shrinkage, settlement and plastic shrinkage cracking were more severe in the presence of higher initial concrete and ambient temperatures even though the critical period and setting times were reduced due to an increase in the concrete temperature. Finally, the surface temperature of the concrete as tested in slabs up to 100 mm in thickness can be used as a good indication of the temperature development in the lower layers of the concrete.

Modelling the cracking of fresh concrete

The cracking of fresh concrete, while still in a plastic state, includes both plastic settlement and plastic shrinkage cracking, which starts once the concrete is cast to around the final setting time. The cracking process is complex and is influenced by numerous factors which include the climate, mix proportions, element geometry and construction procedures. Preventing these cracks therefore remains a problem in practice. One of the reasons for this is the lack of a model that can be used to determine the location, timing and severity of the cracking before the cracking occurs. The main challenges with such a model are the testing of the fresh concrete to determine the tensile material properties, the appropriate constitutive law needed, and the time dependency of material properties as well as the anisotropic volume change. This paper presents a finite element model that uses a total strain smeared cracking approach and accounts for both the time dependency of material properties and the anisotropic volume change. The model gives an adequate representation of the cracking behaviour of fresh concrete for extreme climates but not for normal to moderate climates, mainly due to the size discrepancy between the interior and surface cracks during experiments as well as the relaxation of stresses that are not accounted for in the model. A parameter study showed that both the settlement and shrinkage strains significantly influence and therefore govern the size of the final plastic crack, while the material mechanical properties only influence the time of crack onset and rate of crack widening.

Direct causality between film formation and water-retaining effect of surfactant-based film-forming curing compound for concrete

Surfactant-based film-forming curing compounds (SFCCs) are widely used to retain water on fresh concrete by forming multilayered films. However, the water-retaining mechanism is not yet fully understood; therefore, we aimed to clarify this mechanism, thereby potentially aiding in evaluating the effect of SFCC or to develop more effective SFCCs. It was confirmed that SFCC does not hinder the setting and hardening properties or strength development. Thus, we examined water evaporation from cement pastes on which SFCC was sprayed. Consequently, the water-retaining effect lasted up to 8 h, which indicating that 8 h after spraying SFCC is enough time for suppression of plastic cracking. We then observed the water surface on which SFCC was spread under a Brewster angle microscope and discovered that SFCC on the water surface forms continuous thin film and agglomerates. The water-retaining effect was higher when a continuous thin film was formed; thus, the observation of this thin film facilitated the evaluation of the effect of SFCC. • This study focused on a surfactant-based film-forming curing compound (SFCC). • The water-retaining effect of SFCC continued up to 8 h. • SFCC on the water surface forms continuous thin film and agglomerates. • The water-retaining effect was higher when the continuous thin film was formed.

Study on Performance of Wax Warm Mix Asphalt Cracked by Mixed Polyethylene Waste Plastics

In order to study the modified performance of polyethylene waste plastic cracking wax on asphalt, this paper prepared polyethylene wax (PE wax) by catalytic cracking using waste polyethylene as raw material and Ni-based zeolite as catalyst in a pressure reactor under closed conditions. 70# base asphalt was modified with PE wax, and the properties of pyrolysis wax on asphalt under different catalytic cracking time were studied by three indexes test, Brinoll rotary viscosity test, DSC test and dynamic shear rheology test. The test results show that the cracking products of mixed polyethylene waste plastic cracking wax have good viscosity reduction effect on asphalt under different cracking time. After modification, the high temperature performance of asphalt is improved, and the low temperature performance has a certain influence, but it still meets the specification requirements; In the temperature range of 0°C~60°C, the addition of pyrolysis wax can make the phase transformation of matr-ix asphalt more stable.

Liquid fuel oil produced from plastic based medical wastes by thermal cracking

The present work is an effort to produce liquid fuel oil from plastic based medical wastes through thermal cracking process under oxidizing conditions. The mixed plastics from medical wastes were considered as a feedstock, shredded into small pieces and heated at 773 ± 10 K for 40 min with a heating rate of 20 K/min in a batch reactor for thermal cracking process. The feedstock was characterized by proximate and ultimate analysis along with thermogravimetric investigation. Moreover, chemical compositions of the liquid fuel oil were examined by FTIR and GC–MS spectroscopy. The properties of liquid product were also examined and compared to the commercial fuel oil. The average yield of brownish and sticky liquid fuel was obtained to be 52 wt% and the gross calorific value of the liquid was found 41.32 MJ/kg which is comparable to that of commercial diesel. FTIR spectrum showed characteristic absorption bands of C–H and =CH2 groups indicating presence of alkane and alkene compounds. GC–MS study demonstrated the chemical constituents of the liquid product that is mostly aliphatic compounds of mainly alkanes (16.28%), alkenes (10.67%), alcohols (14.65%) and ester groups (10.38%) including iso-phthalate (40.02%) as a predominant product. This experiment concludes that the liquid oil derived from thermal cracking of mixed plastics comprised of a composite mixture of organic components. A significant amount of non-degraded constituents like plasticizers, precursors, etc. remained in the product having some economic values with human health and environmental impacts during burning has been addressed in the current issue.

Elastic-Plastic Analytical Solution for SEMI’s Horizontal Brace with a Circumferential Through Crack under Tension and Bending

The elastic-plastic behavior of semi-submersible’s horizontal brace with a circumferential through crack which lies at its boundary was studied. Both tension and bending were considered to investigate the closed-form analytical solution. The results indicate that the tensile plastic zone and crack tip opening displacement (CTOD) on the cracked section increase sharply after a smoothly increment when loads became larger. The cracked horizontal brace with a greater initial circumferential through crack has a larger tensile plastic zone and earlier compressive plastic zone appearance on the cracked section. Compared with the load of tension, the bending load has larger effect on the plastic zones of the cracked section and CTOD of the crack. Introduction Since the first semi-submersible platform (SEMI) named as “Ocean Driller” which was designed for drilling wells in the ocean, the SEMIs have gained popularity in the recent decades with ongoing development in oil and natural gas exploration in deepwater. Because of the high risk of environment pollution and casualties of operators which a destruction accident of SEMI might bring, making sure the structure is safe during its service life has become the most important task of SEMI designers and operators. Although the safety design standards for SEMI structures are quite strict, cracks inescapably are initiated during their service life. According to the destruction accidents happened before, Moan (2009) and Zaron et al. (2015) found that the cracks often occur at the horizontal braces which function as the supporting structures in SEMIs and bear complex loads. The presence of such cracks at critical locations can compromise the safety of the braces and then can cause serious disaster eventually. Because of the initial fracture of a horizontal brace, e.g., the accident of Alexander Kielland platform, the loads were transferred to the other braces and led them break because of the overload (see Colin et al. [2014]).

Plastic shrinkage and cracking of 3D printed mortar with recycled sand

This study focused on the plastic shrinkage and cracking of 3D printed mortar mixed with recycled sand as fine aggregates. The test methods for free and restrained plastic shrinkage were designed and improved to simulate the plastic shrinkage of 3D printed mortar. The shrinkage and the development of cracks under constraints were measured by image processing, and the effect of recycled sand was evaluated. 3D printed natural sand mortar and 3D printed recycled sand mortar with replacement ratios of 25%, 50%,75%, and 100% were tested and analyzed. Results showed that the plastic shrinkage of the 3D printed mortar increased with the increase of recycled sand content. With the higher replacement ratio of recycled sand, the plastic cracking of 3D printed mortar under restraint conditions showed a higher cracking depth. It can be concluded that the 3D printed mortar mixed with recycled sand shows a minor plastic shrinkage rate under a 50% replacement ratio. When a 100% replacement ratio of recycled sand is reached, the 3D printed recycled sand mortar needs additional consideration of shrinkage compensation design to avoid early-age cracking in the plastic stage.

Sectional analysis of the cyclic behavior of steel fiber reinforced concrete

AbstractSteel fiber reinforced concrete (SFRC) is known for improving the tensile post‐cracking fatigue behavior of concrete. This paper presents a method to obtain the cyclic tensile behavior of SFRC through sectional analysis, using a limited amount of input parameters. The analytical model is divided into two parts: a monotonic and cyclic model. The monotonic model calculates the uniaxial stress‐crack width curves or constitutive laws of SFRC that fulfill the beam's equilibrium with the smallest error. Afterwards, when the constitutive law is known, the cyclic model predicts the behavior during progressive load cycles. Two methods are used to implement the damage caused by cyclic loading: based on the experimental stiffness during cyclic direct tensile tests (DTTs) and based on a relation between the plastic crack width and the crack width at unloading. The latter option is preferred as no additional DTTs are needed. The proposed methodology therefore eliminates the need for challenging DTTs and only requires more feasible monotonic three‐point bending tests (3PBTs) for model calibration. The model is validated by means of DTTs and cyclic 3PBTs and its potential for extension to fatigue loading is shown.

A detailed study of mode II test specimen with elastic or plastic crack tips by using boundary element method

In linear elastic fracture mechanics the stress and strain magnification at the crack tip is characterized by stress intensity factors which have been obtained for a large variety of loading and specimen geometries and of course mode II test specimen included. In this paper not only different kinds of boundary conditions of the contact surfaces of the elastic crack tip will be discussed but the plastic one. The rotation of the center line of the specimen will also be discussed. The results show the powerful application of the BEM model in the specimen.

Influence of the Feedstock on the Process Parameters, Product Composition and Pilot-Scale Cracking of Plastics.

Chemical recycling of polymers can lead to many different products and play a significant role in the circular economy through the use of plastic waste as a feedstock in the production of valuable materials. The polyolefins: polyethylene (PE) and polypropylene (PP), together with polystyrene (PS), can be chemically recycled by the thermal cracking (pyrolysis) process. In this study, continuous cracking of polyolefins and polystyrene in different proportions and with the addition of other polymers, like polyethylene terephthalate (PET) and polyvinyl chloride (PVC), was investigated at the pilot scale in terms of the process parameters and product yields. Gas chromatography with mass spectrometry (GC-MS) was used for the detailed analysis of the products’ compositions. The boiling temperature distribution and the bromine number were used for additional characterization of products. It was found that an increase of PP share caused a decrease in the process temperature, an increase of the product yield and a shift of the boiling range towards lighter products, increasing the content levels for unsaturates and branched hydrocarbons. It was observed that the addition of 5% PS, PET and PVC reduced the overall product yield, resulting in the creation of a lower-boiling product and increasing the conversion of polyethylene. An addition of 10% polystyrene increased the PP conversion and resulted in a higher product yield, without significant change in the boiling temperatures distribution.

A high-fidelity crystal-plasticity finite element methodology for low-cycle fatigue using automatic electron backscatter diffraction scan conversion: Application to hot-rolled cobalt–chromium alloy

The common approach to crystal-plasticity finite element modeling for load-bearing prediction of metallic structures involves the simulation of simplified grain morphology and substructure detail. This paper details a methodology for predicting the structure–property effect of as-manufactured microstructure, including true grain morphology and orientation, on cyclic plasticity, and fatigue crack initiation in biomedical-grade CoCr alloy. The methodology generates high-fidelity crystal-plasticity finite element models, by directly converting measured electron backscatter diffraction metal microstructure grain maps into finite element microstructural models, and thus captures essential grain definition for improved microstructure–property analyses. This electron backscatter diffraction-based method for crystal-plasticity finite element model generation is shown to give approximately 10% improved agreement for fatigue life prediction, compared with the more commonly used Voronoi tessellation method. However, the added microstructural detail available in electron backscatter diffraction–crystal-plasticity finite element did not significantly alter the bulk stress–strain response prediction, compared to Voronoi tessellation–crystal-plasticity finite element. The new electron backscatter diffraction-based method within a strain-gradient crystal-plasticity finite element model is also applied to predict measured grain size effects for cyclic plasticity and fatigue crack initiation, and shows the concentration of geometrically necessary dislocations around true grain boundaries, with smaller grain samples exhibiting higher overall geometrically necessary dislocations concentrations. In addition, minimum model sizes for Voronoi tessellation–crystal-plasticity finite element and electron backscatter diffraction–crystal-plasticity finite element models are proposed for cyclic hysteresis and fatigue crack initiation prediction.

Comparison of safety margin in LBB design of nuclear pipes based on various types of fracture resistance test specimens

The geometry of cracked pipe, loading condition and crack size all can have a strong effect on its resistance against crack-tip plastic deformation and crack growth. Usually, specimens listed in test standards (e.g. CT specimen) are applied to evaluate the fracture resistance (J-R) curves, which may cause excessive safety margin in leak-before-break (LBB) design of nuclear pipes. In this study, standard (CT) specimen and constraint designed specimens, including curved CT and compact pipe (CP) specimens were applied to measure the J-R curves of nuclear pipes. Finite element analysis (FEA) was applied to derive J-equations to calculate J-R curves for newly designed specimens. Constraint effects in these specimens and full-scale pipes under various loading conditions were compared according to crack-tip plastic deformation level. Then, safety margins in LBB design using these specimens were quantitatively analyzed by constructing the critical crack length lines. Both the tests and FEA results verified the validity of these constraint designed specimens for reducing conservatism.