Constraint comparisons for common fracture specimens: C(T)s and SE(B)s

New testing standards (e.g., ASTM E1921) remain under continuing development to measure the fracture toughness of ferritic steels over the ductile-to-brittle transition. The procedures assume that relatively small, deep-notch test specimens maintain near small-scale yielding conditions at fracture, which simplifies greatly the interpretation of measured values. However, 3-D finite element analyses suggest that the geometry and small size of common fracture specimens leads frequently to constraint loss, e.g., the decay of small-scale yielding conditions, at only moderate levels of deformation. The Weibull stress micromechanical model, or “local approach,” is employed here to quantify these constraint effects. Previous research along these same lines quantifies constraint loss in common fracture specimens relative to strict plane-strain, small-scale yielding conditions with a zero T-stress. Here we present a more practical approach for application within experimental testing programs by comparing directly the two most commonly tested fracture specimens, the single-edge notched bend, SE(B), and the compact tension, C(T), specimens. Developers of testing standards may thus choose a “reference” specimen then correct values measured with other specimens to the adopted reference configuration.     

The effect of fatigue pre‐cracking forces on fracture toughness

Testing procedures for the determination of the fracture toughness of a material by monotonic loading of fatigue pre‐cracked specimens are well established in standards such as BS 7448, BS EN ISO 15653, ISO 12135, ASTM E1820 and ASTM E1921. However, a review of these standards indicates a wide range of permitted fatigue pre‐cracking forces, whilst the underlying assumption in each standard is that the pre‐cracking conditions do not affect the fracture toughness determined. In order to establish the influence of different fatigue pre‐cracking forces on the fracture toughness, tests were carried out on specimens from an API 5L X70 pipeline steel. Single‐edge notch bend specimens of Bx2B geometry were notched through thickness and tested at temperatures of +20 °C, ?80 °C and ?140 °C to show the fracture behaviour in different regions of the fracture toughness ductile‐to‐brittle transition curve. Fatigue pre‐cracking was conducted on a high‐frequency resonance fatigue test machine over a range of pre‐cracking forces permissible within the various standards and beyond. The results showed that an excessively high pre‐cracking force can result in a significant overestimation of the value of fracture toughness for material exhibiting brittle behaviour, whilst very low fatigue pre‐cracking forces appeared to result in an increase in scatter of fracture toughness. A review of standards indicated that there was a possibility to misinterpret the intention of the ISO 12135 standard and potentially use excessively high pre‐cracking forces. Suggested clarifications to this standard have therefore been proposed to avoid the risk of overestimating fracture toughness.     

Experimental techniques for fracture instability toughness determination of unidirectional fibre metal laminates

ABSTRACT The aim of this work is to propose procedures for the measurement of the fracture toughness of fibre metal laminates (FMLs) reinforced with unidirectional fibres of aramid or glass. Experimental techniques for fracture toughness evaluation by using Compact (C(T)) and Single‐Edge Bend (SE(B)) specimens obeying ASTM standards are introduced. Procedures from the standard for thick metallic materials were modified in order to overcome problems, which can arise when testing FMLs – that is, specimen buckling, indentations and crack growth in planes other than the plane of the fatigue pre‐crack or notch. The methodology proposed was experimentally tested leading to satisfactory results.     

Residual strength of unidirectional fibre-metal laminates based on JC toughness of C(T) and SE(B) specimens: comparison with M(T) test results

Fibre‐metal laminates (FMLs) are structural composites designed with the aim of producing very low fatigue crack‐propagation rate, damage‐tolerant and high‐strength materials, if compared to aeronautical Al alloys. Their application in aeronautical structures demands a deep knowledge of a wide set of mechanical properties and technological values, including both fracture toughness and residual strength. The residual strength of FMLs have been traditionally determined by using wide centre‐cracked tension panels M(T). The use of this geometry requires large quantities of material and heavy laboratory facilities. In this work, fracture toughness ( J_C) of some unidirectional FMLs laminates was measured using a recently proposed methodology for critical fracture toughness evaluation on compact tension C(T) and single‐edge bend SE(B) specimens. Additionally, residual strength values of wider M(T) specimens with different widths (W from 150 to 200 mm) and several crack to width ratios (2a/W) were experimentally obtained. Some experimental residual strength values of M(T) specimens (W from 150 to 400 mm and different 2a/W ratios) of Arall were also obtained from the bibliography. Based on J_C results from C(T) and SE(B) specimens, and either using or not using crack‐tip plasticity corrections, the residual strengths of the M(T) specimens were predicted and compared to the experimental ones. The results showed good agreement, especially when crack‐tip plasticity corrections were applied.     

Numerical investigation of 3-D constraint effects on brittle fracture in SE(B) and C(T) specimens

Specimen size and geometry effects on cleavage fracture of ferritic steels tested in the ductile-to-brittle transition region remain an important technological impediment in industrial applications of fracture mechanics and in the on-going development of consensus fracture testing standards. This investigation employs 3-D nonllinear finite element analyses to conduct an extensive parametric evaluation of crack front stress triaxiality for deep notch SE(B) and C(T) specimens and shallow notch SE(B) specimens, with and without side grooves. Crack front conditions are characterized in terms of J-Q trajectories and the constraint model for cleavage fracture toughness proposed previously by Dodds and Anderson. An extension of the toughness scaling model suggested here combines a revised in-plane constraint correction with an explicit thickness correction derived from extreme value statistics. The 3-D analyses provide effective thicknesses for use in the statistical correction which reflect the interaction of material flow properties and specimen aspect ratios, a/W and W/B, on the varying levels of stress triaxiality over the crack front. The 3-D computational results imply that a significantly less strict size/deformation limit, relative to the limit indicated by previous plane-strain computations, is needed to maintain small-scale yielding conditions at fracture by a stress-controlled, cleavage mechanism in deep notch SE(B) and C(T) speciments. Moreover, the analyses indicate that side grooves (20 percent) should have essentially no net effect on measured toughness values of such specimens. Additional new results made available from the 3-D analyses also include revised -plastic factors for use in experimental studies to convert measured work quantities to thickness average and maximum (local) J-values over the crack front. To estimate CTOD values, new m-factors are included for use in the expression 131-1.     

Quantifying Tstress controlled constraint by the master curve transition temperature T0

Specimen size, crack depth and loading conditions may effect the materials fracture toughness. In order to safeguard against these geometry effects, fracture toughness testing standards prescribe the use of highly constrained deep cracked bend specimens having a sufficient size to guarantee conservative fracture toughness values. One of the more advanced testing standards, for brittle fracture, is the master curve standard ASTM E1921-97, which is based on technology developed at VTT Manufacturing Technology. When applied to a structure with low constraint geometry, the standard fracture toughness estimates may lead to strongly over-conservative estimate of structural performance. In some cases, this may lead to unnecessary repairs or even to an early “retirement” of the structure. In the case of brittle fracture, essentially three different methods to quantify constraint have been proposed, J small scale yielding correction, Q-parameter and the T_stress. Here, a relation between the T_stress and the master curve transition temperature T₀ is experimentally developed and verified. As a result, a new engineering tool to assess low constraint geometries with respect to brittle fracture has been obtained.     

Corrected stress intensity factor solution for a British standard single edge notched tension (SENT) specimen

This paper revisits a complicated analytical solution of the stress intensity factor K adopted in a newly published British standard BS 8571:2014 for clamped single edge notched tension (SENT) specimens. Comparison with existing numerical results of K shows that the analytical K solution in BS 8571 is correct only for the crack length to specimen width ratio a/W ≤ 0.6, but incorrect for a/W > 0.6. A reinvestigation is thus performed using the crack compliance method, and a corrected K solution is obtained for the BS 8571 clamped SENT specimens over the full range of a/W. On this basis, a simple closed‐form solution of K is obtained using the best curve fitting with an accuracy within 1% for crack sizes up to a/W = 0.98. Results show that the proposed closed‐form solution of K agrees well with the numerical results of K for the clamped SENT specimens.     

Determination of constraint limits for cleavage initiated toughness data

The proper constraint limits for cleavage initiated toughness data within the ductile-to-brittle transition regime have been studied extensively using both numerical analysis and analysis of experimental data. Historically, the experimentally based constraint limits have supported less conservative limits. This study conducts analysis of existing and new experimental data developed using data sets targeted to exhibit constraint loss toughness enhancement. Constraint herein is quantified in terms of the scaled specimen deformation level, more commonly known as M. It is expected that data with low M values will exhibit the greatest affect of constraint loss. Large data sets are therefore developed and extracted from the literature that include data with a large range of M levels and at least the required number of uncensored results with M > 30 for valid T₀ measurement as per ASTM E1921-02. Differences in the calculated T₀ values using censoring limits of 5-500 are then determined. The onset of T_lim differences due to constraint loss is examined by simply increasing the censoring limit, M_lim, utilized in determining the indexing temperature, T_lim, and evaluating differences between T₀ and the T_lim values obtained using higher constraint limits. Bias resulting from this censoring procedure is examined using a Monte-Carlo analysis and shown to be small.Measurement of a high constraint T₀ in bend specimens is shown to require M_lim > 200. As M_lim increases from 30 to 200 in bend specimens, the corresponding T_lim can increase by approximately 15 °C. Further increases in M_lim do not result in substantial increases in T_lim. This evolution buttresses previous numerical findings by Dodds and co-workers [Specimen size requirements for fracture toughness testing in the ductile-to-brittle transition regime, J Test Eval 1991;191:123-34; Size and deformation limits to maintain constraint in K_Ic and J_c testing of bend specimens. In: Kirk M, Ad Bakker, editors. Constraint effects in fracture theory and applications: second volume. ASTM STP 1244, 1995; Numerical investigation of 3-D constraint effects on brittle fracture in SE(B) and C(T) specimens, Int J Fract 1995;74:131-61] and provides a strong justification for changes to ASTM E1921-02 if a conservative, geometry insensitive, and transferable reference temperature, T₀, is to be determined using this standard. Possible short-term changes to ASTM E1921-02 could include raising M_lim and requiring an upward shift of SE(B) T₀ values. A more desirable solution is to adjust individual K_Jc toughness values before evaluation of T₀ to eliminate specimen geometry bias.     

Comparison of using the crack mouth displacement (CMOD) and load line displacement (LLD) methods in the determination of critical J integral in SENB specimens

Various methods for direct and indirect determination of LLD and CMOD were used to determine J from SENB specimens in three different steels. The influence of the displacement measurement on J is discussed, and shows that the values of J using LLD determined from clip gauge methods to the ASTM E1820 or ISO 12135 standards are consistent with values of J determined from CMOD (either directly or using clip gauge methods), as defined in ASTM E1820. From this work it is recommended that standard methods such as ISO 12135 should permit load‐CMOD and load‐LLD as alternative methods to determine J. Methods to determine LLD by corrections to the ram displacement were also shown to be effective in determining J, for applications where the use of clip gauges may be challenging, such as fracture toughness testing in sour environments, dynamic tests, or testing at very high temperature.     

Correlation of fracture behavior in high pressure pipelines with axial flaws using constraint designed test specimens--Part I: Plane-strain analyses

This work presents a numerical investigation of crack-tip constraint for SE(T) specimens and axially surface cracked pipes using plane-strain, nonlinear computations. The primary objective is to gain some understanding of the potential applicability of constraint designed fracture specimens in defect assessments of pressurized pipelines and cylindrical vessels. The present study builds upon the J-Q approach using plane-strain solutions to characterize effects of constraint on cleavage fracture behavior for the analyzed fracture specimens and cracked pipes. Under increased loading, each cracked configuration follows a characteristic J-Q trajectory which enables comparison of the corresponding driving force curve in the present context. A key outcome of this investigation is that toughness data measured using SE(T) specimens appear more applicable for cleavage fracture predictions of pressurized pipelines and cylindrical vessels than standard, deep notch fracture specimens under bend loading. The results provide a strong support for use of constraint-designed SE(T) specimens in fracture assessments of pressurized pipes and cylindrical vessels.     

Mode-I fracture toughness testing of thick section FRP composites using the ESE(T) specimen

Experimental and numerical analyses are performed to determine the translayer mode-I fracture toughness of a thick-section fiber reinforced polymeric composite using the eccentrically loaded, single-edge-notch tension, ESE(T) specimen. Finite element analyses using the virtual crack closure technique were performed to assess the effect of material orthotropy on the mode-I stress intensity factors in the ESE(T) specimen. The stress intensity factors for the proposed ESE(T) geometry, are calculated as a function of the material orthotropic parameters. The formula is validated for a class of thick composite materials. The thick composite tested in this study is a pultruded composite material that consists of roving and continuous filament mat layers with E-glass fiber and polyester matrix materials. Data reduction from the fracture tests was performed using two methods based on existing metallic and composite ASTM [ASTM E 1922, Standard Test Method for Translaminar Fracture Toughness of Laminated Polymer Matrix Composites, Annual Book of ASTM Standards, 1997; ASTM E 399, Standard Test Method for Plane-Strain Fracture Toughness of Metallic Materials, Annual Book of ASTM Standards, 1997] fracture testing standards. Criteria for assessing test validity and for determining the critical load used in calculating the fracture toughness were examined. Crack growth measurements were performed to determine the amount of stable crack growth before reaching critical load. The load versus notch mouth opening displacement, for different crack length to width ratios is affected by material orthotropy, nonlinearity, and stable crack propagation. The mode-I translayer fracture toughness and response during crack growth is reported for ESE(T) specimen with roving layers oriented both, transverse and parallel to the loading direction.     

J-Resistance curve testing of HY80 steel using SE(B) specimens and normalization method

The normalization method is adopted for standard and nonstandard specimens in this paper to develop J-R curves for HY80 steel directly from load versus load-line displacement records without use of automatic crack length measurement. The standard specimens usually contain high crack-tip constraints, while the nonstandard specimens involve low crack-tip constraints. To obtain J-R curves with different constraints, a series of single edge notched bend (SE(B)) specimens with different crack lengths for an HY80 steel are tested in accordance with ASTM standard E1820. The normalization method is then used for determining crack extension and J-R curves for these SE(B) specimens.To validate the normalization method, the J-R curves determined using the normalization method are compared with those obtained by the elastic unloading compliance method for the SE(B) specimens. The comparison shows that good agreements exist between the two methods, and the normalization method is a viable tool to be used to determine J-R curves of the HY80 steel for the standard as well as nonstandard SE(B) specimens. In the J-integral calculations, the resistance curve test method, the basic test method and the modified basic test method specified in ASTM E1820 are evaluated. The results indicate that the modified basic method can be equivalent to the resistance curve method.     

Evaluation of the two‐parameter fracture criterion for various crack configurations made of 7075‐T6 aluminium alloy using finite‐element fracture simulations

For many years, a two‐parameter fracture criterion (TPFC) has been used to correlate and predict failure loads on cracked metallic fracture specimens. The current study was conducted to evaluate the use of the TPFC on a high‐strength aluminium alloy, using elastic‐plastic finite‐element (FE) analyses with the critical crack‐tip‐opening angle (CTOA) fracture criterion. In 1966, Forman generated fracture data on middle‐crack tension, M(T), specimens made of thin‐sheet 7075‐T6 aluminium alloy, which is a quasi‐brittle material. The fracture data included a wide range of specimen half‐widths (w) ranging from 38 to 305 mm. A two‐dimensional FE analysis code (ZIP2D) with a “plane‐strain core” option was used to model the fracture process with a critical CTOA chosen to fit the M(T) test data. Fracture simulations were then conducted on other M(T), single‐edge‐crack tension, SE(T), and bend, SE(B), specimens over a wide range in widths (w = 19‐610 mm). No test data were available on the SE‐type specimens. The results supported the TPFC equation for net‐section stresses less than the material proportional limit. However, some discrepancies in the FE fracture simulations results were observed among the numerical analyses made on the three specimen types. Thus, more research is needed to improve the transferability of the TPFC from the M(T) specimen to both the SE(T) and SE(B) specimens for quasi‐brittle materials.     

Effects of Fibre Geometry and Volume Fraction on the Flexural Behaviour of Steel‐Fibre Reinforced Concrete

Abstract: This work aims in studying the mechanical behaviour of concrete, reinforced with steel fibres of different geometry and volume fraction. Experiments include compression tests and four‐point bending tests. Slump and air content tests were performed on fresh concrete. The flexural toughness, flexural strength and residual strength factors of the beam specimens were evaluated in accordance with ASTM C1609/C1609M‐05 standard. Improvement in the mechanical properties, in particular the toughness, was observed with the increase of the volume fraction of steel‐fibres in the concrete. The fibre geometry was found to be a key factor affecting the mechanical performance of the material.     

Effects of weld strength mismatch on <Emphasis Type="Italic">J</Emphasis> and CTOD estimation procedure for SE(B) specimens

This work examines the effect of weld strength mismatch on fracture toughness measurements defined by J and CTOD fracture parameters using single edge notch bend (SE(B)) specimens. A central objective of the present study is to enlarge on previous developments of J and CTOD estimation procedures for welded bend specimens based upon plastic eta factors (η) and plastic rotational factors (r _p ). Very detailed non-linear finite element analyses for plane-strain models of standard SE(B) fracture specimens with a notch located at the center of square groove welds and in the heat affected zone provide the evolution of load with increased crack mouth opening displacement required for the estimation procedure. One key result emerging from the analyses is that levels of weld strength mismatch within the range ±20% mismatch do not affect significantly J and CTOD estimation expressions applicable to homogeneous materials, particularly for deeply cracked fracture specimens with relatively large weld grooves. The present study provides additional understanding on the effect of weld strength mismatch on J and CTOD toughness measurements while, at the same time, adding a fairly extensive body of results to determine parameters J and CTOD for different materials using bend specimens with varying geometries and mismatch levels.     

Evaluation of the Mechanical Properties of Reinforcing Steel Bars from Collapsed Building Sites

Mechanical properties of reinforcing steel bars obtained from three different collapsed building sites in Lagos, Nigeria were examined. An optical emission spectrometer was used for chemical composition analysis while the tensile test was carried out using a Universal Testing Machine. The yield strength of the steel bars was found to be higher than BS4449 (GRADE 460B), Nst.65-Mn, and ASTM A706 standards, while their percentage elongations were lower than most of the standards. The steel bars used at the Sango collapse site have higher UTS compared with the standards, while those used at Ilesanmi and Ewuntun collapse sites have UTS values that are in close range with the standards. The reinforcing bar obtained from Ilesanmi collapsed site has higher percentage elongation than ASTM A706 standard but lower than Nst.65-Mn and BS4449 (GRADE 460B) standards. The bars obtained from Sango and Ewuntun collapse sites displayed lower percentage elongation compared with that from Ilesanmi site. All the investigated reinforcing bars possessed reasonably high strength with low ductility. Thus, these bars are susceptible to brittle fracture, which might have contributed to the collapse of the building structures.     

Plastic limit load and its application to the fracture toughness testing for heterogeneous single edge notch tension specimens

The current investigation pursues the confirmation of the applicability of the limit load solutions in determination of the η factors necessary for fracture toughness testing protocols. The procedure begins with the correct calculation of limit load values in welded single edge notch tension (SE(T)) fracture specimens containing centreline cracks. Hence, the η factor is inferred through the principle of potential energy. Additionally, such results are compared with those obtained from finite element analyses, including strain hardening effects available in the literature. SE(T) specimens subject to pin‐loading display that the η factors are insensitive to the configurational effects and hardening properties. On the other hand, in clamped SE(T) specimens, such effects become meaningful, making its usage in fracture toughness experiments questionable. This work provides an alternative methodology to compute fully plastic proportionality coefficients (η) based on limit load solutions for heterogeneous cracked SE(T) specimens. These analyses also consider the limitations and potentialities of such an approach in experimental measurements of ductile crack growth.     

A new method for determining the fracture toughness of main pipeline steels

One of the fundamental aims of fracture mechanics is to define fracture toughness K_IC of a material. Hence, the ASTM E399 standard was developed. However according to the standard, large‐sized specimens are required to determine the fracture toughness of low alloy carbon steels. ASTM E1921 standard was developed on the fracture toughness of ferritic steels. In this study, a new method was proposed to determine the fracture toughness of ferritic steels. The purpose of the present paper is to compare the results of the method with the experimental results. Two steels that are used in gas and oil main pipelines were investigated in this study.     

Numerical investigation on J-integral testing of heterogeneous fracture toughness testing specimens: Part I – weld metal cracks

Based on extensive two‐dimensional (2D) finite element (FE) analyses, the present work provides the plastic η factor solutions for fracture toughness J‐integral testing of heterogeneous specimens with weldments. Solutions cover practically interesting ranges of strength mismatch and relative weld width, and are given for three typical geometries for toughness testing: a middle cracked tension (M(T)) specimen, single edge cracked bend (SE(B)) specimen and (C(T)) specimen. For mismatched M(T) specimens, both plane strain and plane stress conditions are considered, whereas for SE(B) and C(T) specimens, only the plane strain condition is considered. For all cases, only deep cracks are considered, and an idealized butt weld configuration is considered, where the weld metal strip has a rectangular cross section. Based on the present solutions for the strength mismatch effect on plastic η factors, a window is provided, within which the homogeneous J estimation procedure can be used for weldment toughness testing. The effect of the weld groove configuration on the plastic η factor is briefly discussed, concluding the need for further systematic analysis to provide guidance to practical toughness testing.