THE EFFECT OF SPECIMEN SIZE ON THE CTOD R-CURVE BEHAVIOUR OF A TITANIUM ALLOY

Abstract— —This paper presents preliminary results from a large experimental programme to study geometry and size effects in CTOD R-curves. The results presented were obtained from unloading compliance R-curve tests performed at room temperature on different sized single-edge-notch bend specimens made from Ti–3Al–2V alloy. The crack growth resistance was measured in terms of both the conventional CTOD, δ₀, (i.e. as defined in BS 5762) and CTOD corrected for crack growth, δ_R . It was found that the δ₀ and δ_R R-curves were independent of specimen size up to crack extensions corresponding to approximately 10–15% of the original uncracked ligament. Also, after crack extensions of 30–40% of the initial ligament the δ₀ and δ_R R-curves exhibited well defined upswings. The upswing in the CTOD R-curves is thought to be a result of a reduction in crack tip constraint.     

Mode I intra-laminar crack growth in composites — modelling of R-curves from measured bridging laws

In this paper R-curves for mode I crack growth in composites are modelled based on measured bridging laws. It is shown that simulated and measured R-curves are in good agreement. Simulations show that variations in the measured bridging law parameters can explain the scatter in overall R-curves. Finite element procedures for treating a generalised nonlinear law for intra-laminar fibre bridging (longitudinal splitting) in combination with R-curve modelling are demonstrated for mode I loading. The difference between calculating the crack growth resistance by linear elastic fracture mechanics and by the J integral for the double cantilever beam specimen loaded by wedge forces is elucidated. It is shown that calculating the crack growth resistance by linear elastic fracture mechanics results in overestimation of the steady-state crack growth resistance.     

R-curves characterisation analysis for asphalt concrete

Fracture tests, especially at lower testing temperatures, have become quite popular in quantifying low-temperature cracking. However, current fracture testing analysis methods often use a single number, such as fracture energy or fracture toughness, to quantify cracking resistance. These tests do not capture both the initiation and propagation of the crack. The Resistance Curve, or R-curve, is widely applied in many fields, such as metal, polymer and composites. The R-curve considers cracking resistance as a function of crack extension, which includes initiation and propagation. In this research, three asphalt concrete mixtures, including hot mix, hot mix with reclaimed asphalt pavement (RAP) and warm mix with RAP were tested at two temperatures, three levels of ageing and two levels of moisture condition by the Semi-Circular Bend fracture test. R-curves were constructed using the data from the fracture test, and digital images were utilised to capture the crack extension. In addition to capturing the traditional fracture energy, two new parameters were explored using the R-curves: the cohesive energy and the propagation parameter energy rate. It was found that cohesive energy was always in a narrow range (approximately 500–1000 J/m²) compared to the fracture energy range (approximately 500–1700 J/m²) over all combinations of ageing and moisture conditions, which indicates that the crack initiation may not be as sensitive to temperature, ageing and moisture as fracture energy. The results of energy rate indicated that moisture and short-term ageing impact the crack propagation by reducing the resistance of crack growth. These results proved that R-curves are a potentially useful tool to quantify the cracking resistance of asphalt concrete in both crack initiation and propagation.     

A STUDY OF SPECIMEN SIZE ON J-R CURVE BEHAVIOUR

This paper presents results from an experimental programme to study size effects in J-R curves. Results are presented from unloading compliance R curve tests on different sized single edge notch bend specimens of nickel aluminium bronze and compared with previously published R curve data on a Ti3A1-2.5V titanium and an HY 100 steel alloy. The crack growth resistance was measured in terms of the standard fracture resistance J, J corrected for crack growth and the J modified parameter proposed by Ernst. It was observed that following a region of size independence small specimen J-R curves could fall either above or below the large specimen curve. It was found that although the limit to J controlled crack growth could be extended the limit is not unique but dependent on material type.     

Different R-Curves for Two- and Three-Dimensional Cracks

R-curves caused by crack face interactions are important for the strength assessment of components with small cracks. Whereas an influence of the initial crack length on the R-curve is well understood on the basis of fracture mechanics, it will be shown here that also the type of the crack affects the crack growth resistance. For a given crack-bridging relation it can be shown that 3-dimensional cracks as circular internal cracks and semi-circular surface cracks must exhibit a lower R-curve than obtainable from 2-dimensional edge cracks.     

SENSITIVITY ANALYSIS OF THE DOUBLE CLIP GAUGE METHOD

During fracture toughness testing, the stable crack growth measurement is necessary for the construction of the R-curves of J vs Δa or CTOD vs Δa. One possible measurement technique uses the Double Clip Gauge Method, which is based on the assumption that the specimen is deformed like two rigid arms that rotate around an apparent centre of rotation located in front of the crack tip. This apparent centre moves as the crack grows in a stable way, and its position can be estimated through the measurement of two crack opening displacements located at different heights. As a consequence the crack growth can be calculated. In this paper the behaviour of the equations that govern the Double Clip Gauge Method are described, and the zones of greatest sensitivity for the location of the clip gauges are determined. A sensitivity analysis of the most influential intervening variables is also made.     

Comparison of Interlaminar Fracture Toughness in Unidirectional and Woven Roving Marine Composites

This paper investigates the effect of fibre lay-up and matrix toughness on mode I and mode II interlaminar fracture toughness (G_Ic and G_IIc) of marine composites. Unidirectional and woven roving fibres were used as reinforcements. Two vinyl ester resins with different toughness were used as matrices. Results from both modes showed toughness variation that is consistent with matrix toughness. Values of G_Ic were not significantly influenced by fibre lay-up except at peak load points in the woven roving/brittle-matrix composite. Each peak load point, caused by interlocked bridging fibres, signified the onset of unstable crack growth. For unidirectional specimens, crack growth was stable and G_Ic statistically more reliable than woven roving specimens, which gave fewer G_Ic values due to frequent unstable crack growth. Mode II tests revealed that, except for crack initiation, G_IIc was higher in woven roving composites. This was due to fibre bridging, perpendicular to the crack growth direction, which encouraged stable crack growth and increased energy absorption. Mode II R-curves were obtained for the woven roving specimens. These R-curves provide additional information useful for characterising delamination resistance. The paper concludes that composites with woven roving fibres show similar mode I delamination characteristics to the unidirectional composites; but their mode II delamination characteristics, after crack initiation, are quite different.     

Manufacturing Influence on the Delamination Fracture Behavior of the T800H/3900-2 Carbon Fiber Reinforced Polymer Composites

'Torayca' T800H/3900-2 is the first material qualified on Boeing Material Specification (BMS 8-276) which utilizes the thermoplastic-particulate interlayer toughening technology. Two manufacturing processes, the autoclave process and the fast heating rated Quickstep™ process, were employed to cure this material. The Quickstep process is a unique composite production technology which utilizes the fast heat transfer rate of fluid to heat and cure polymer composite components. The manufacturing influence on the mode I delamination fracture toughness of laminates was investigated by performing double cantilever beam tests. The composite specimens fabricated by two processes exhibited dissimilar delamination resistance curves (R-curves) under mode I loading. The initial value of fracture toughness G_IC-INIT was 564 J/m² for the autoclave specimens and 527 J/m² for the Quickstep specimens. However, the average propagation fracture toughness G_IC-PROP was 783 J/m² for the Quickstep specimens, which was 2.6 times of that for the autoclave specimens. The mechanism of fracture occurred during delamination was studied under scanning electron microscope (SEM). Three types of fracture were observed: the interlayer fracture, the interface fracture, and the intralaminar fracture. These three types of fracture played different roles in affecting the delamination resistance curves during the crack growth. More fiber bridging was found in the process of delamination for the Quickstep specimens. Better fiber/matrix adhesion was found in the Quickstep specimens by conducting indentation-debond tests.     

DRAFT EGF RECOMMENDATIONS FOR DETERMINING THE FRACTURE RESISTANCE OF DUCTILE MATERIALS: EGF PROCEDURE EGF P1–87D

Abstract— The EGF Working Party on Fracture Mechanics Testing Standards has written a draft ECF Procedure for determining the crack growth fracture resistance of ductile materials. either in terms of the J-integral or the crack tip opening displacement. Methods are also given for deriving J and δ fracture parameters related to initiation of crack growth. The multiple specimen method is taken as the reference method. Several single specimen techniques are described in Appendices. The EGF Procedure is currently being validated by an experimental round robin.     

Characteristics of Crack Growth in High Performance Concrete Subjected to Fire

An experimental investigation was conducted to identify the characteristics of crack growth in high performance concrete (HPC) subjected to fire, including two parts of work, i.e. crack growth resistance determinations and cracking observations, using concrete of three strength grades 40 MPa, 70 MPa, and 110 MPa. The crack growth resistance curves (R-curves ) of HPC subjected to high temperatures were determined using notched three-point bend beam specimens of 100 mm×100 mm×300mm. The R-curve (crack growth resistance curve) flattening shows that the crack growth resistance has been significantly reduced by elevated temperature. Concrete with a higher strength grade has a steeper R-curve, with a higher fracture toughness but a shorter critical crack growth. The shorter critical crack growth means that concrete of a higher strength grade has a more brittle behavior. The concrete cracking observations reveal that the consequences of rapid heating are quite different from those of slow heating. For slow he     

A MICRO AND MACRO APPROACH TO THE ENERGY DISSIPATION RATE MODEL OF STABLE DUCTILE CRACK GROWTH

The equations for the energy dissipation rate, D per unit area of crack growth, for plasticity and fracture combined, are presented for equilibrium crack extension in a real elastic-plastic material. These relationships are a necessary condition for stable growth. The term D is identical to G for lefm and to the rate at which work is done for the rigid-plastic limit. Crack growth is seen at both micro- and macro-levels as a two stage process of damage accumulation in a process zone followed by actual separation as a micro-instability at the crack tip. Some examples of the behaviour of ductile metals are cited in support at both micro- and macro-level. For the fully plastic case, D reduces strongly with growth. Relationships with conventional rising R-curves are stated for contained and uncontained yield.     

THE SIZE EFFECT OF MICROSTRUCTURAL IMPLICATIONS OF THE WEAKEST LINK MODEL

Abstract— CT specimens made of a reactor pressure vessel steel were loaded at—40°C until final failure occurred by cleavage fracture. The samples of J _lcl values obtained in these tests are analysed using the weakest link model. The size effect observed with specimens of different thicknesses is compared with the predictions of the weakest link model. A formula is derived for the distribution of the locations of fracture origins which have been determined for almost all specimens with a scanning electron microscope. The distribution of the size of the "weak spots" is calculated from the distribution of the fracture origins using two different models for the stress field ahead of the crack tip. These fractographic results and the J _lcl data confirm the basic ideas of the weakest link model. The deviations observed between the quantitative predictions of the weakest link model and the data can partly be explained by the change in the stress state ahead of the crack tip caused by a change in the specimen thickness.     

Ductile crack propagation by plastic collapse of the intervoid ligaments

In the present study ductile crack initiation and propagation is investigated by means of a micro-mechanical model under small-scale yielding conditions. Voids are resolved discretely in the fracture process zone where steep gradients occur during the loading history and are taken into accounted by a homogenized porous plasticity law elsewhere. The size of the region of discrete voids is not set a priori but is determined consistently. The results show that effective crack growth occurs by plastic collapse, i.e. purely geometric softening of the intervoid ligaments without incorporating material separation. Due to this mechanism a limit load exists coinciding with the maximum fracture toughness. In addition, it turns out that the shielding due to the growth of voids around the crack plane has a considerable influence on the computed R-curves compared to models neglecting this effect. Depending on the void arrangement a diffuse softening zone or even crack branching is observed. A comparison with experimental data from literature indicates that plastic collapse and the formation of diffuse zones of void growth are realistic mechanisms of ductile crack propagation.     

Transformation yielding,plasticity and crack-growth-resistance (R-curve) behaviour of CeO2-TZP

Transformation yield and plasticity, transformation zone sizes at crack tips and rising crack-growth-resistance (R-curve) behaviours were studied in a commercial-grade ceria partially stabilized zirconia polycrystalline material (CeO₂-TZP). The yield stresses measured in three-point bending decreased from 390 to 176 MPa when the sintering temperature was varied from 1425 to 1525° C. The corresponding total plastic strain to fracture increased with decreasing yield stress. Crack-tip transformation zones in precracked, annealed and loaded single-edge-notch-bend specimens decreased significantly in size with increasing transformation yield stress; however, the R-curves were relatively insensitive to the yield stresses or the transformation zone sizes. The measured zone sizes and R-curves were examined in terms of both crack shielding and plastic yield strip zone models.     

晶须增韧陶瓷基复合材料裂纹扩展行为模型

在考虑晶须桥联和裂纹转两种增韧机理的基础上，建立了晶须增韧陶瓷复合材料裂纹扩展行为的理论模型，利用该型计算了单边切口梁三点弯曲的Ｒ－阻力曲线和载荷－位移曲线。     

R-curve and subcritical crack growth in lead zirconate titanate ceramics

R-curves and subcritical crack growth curves (V–K_I) were determined for undoped, K doped (PKZT) and Nb doped (PNZT) lead zirconate titanate (PZT) ceramics and the results are discussed including the effect of doping, grain size and the polarisation state. A pronounced crack growth resistance was observed in the soft PNZT ceramic, which is attributed to ferroelastic domain switching. Subcritical crack growth in the studied PZT materials is governed by both environmentally stress-induced corrosion at the crack tip and the crack shielding due to domain switching. Increasing domain switching capacity by structural modification of the material (i.e. by donor doping or by increasing the grain size) or by poling sifts the V–K_I curve to higher values of the stress intensity factor.     

Study of fracture toughness evaluation of FRP

Using the fibre reinforced plastics (FRP) laminates consisting of glass chopped strand mat and unsaturated polyester resin, experiments were conducted under various conditions in order to determine the fracture toughness for crack instability. Crack growth was judged not by cracking of the resin matrix but by break of the glass fibres. The crack front was considered to be located in the section which was cracked through the 90% of the specimen thickness. Crack extension resistance (R-curves) thus obtained did not significantly vary with specimen thickness and initial crack length, but depended greatly on specimen configurations, compact tension (CT) and centre-cracked tension (CCT) specimens. The R-curve for a CT specimen was steeper than the one for a CCT specimen, which is quite contrary to the tendency for metals. It was deduced that the instability fracture toughness calculated from the maximum load on a load-deflection diagram, K _max, was scarcely affected by specimen thickness, initial crack length and specimen geometry (i.e. loading configuration), and therefore could be regarded as a material constant of the FRP used.     

FINITE ELEMENT AND EXPERIMENTAL STUDIES OF CRACK GROWTH IN CLADDED SEN(B) SPECIMENS

Abstract— The transferability of fracture results between homogeneous and cladded specimens was studied in single edge-notched bend specimens. The test material was of A533-B steel with a clad layer deposited by a commercial strip welding process. The fracture resistance properties were developed independently for cladding and base material using homogeneous specimens of each material. The experimental data from tests on cladded specimens were analysed with the finite element method. The 3D J -values were compared with values evaluated using the measured crack extension in the cladded specimen and the J _R-data of the respective material provided from homogeneous specimens. A reasonably good agreement was obtained in this comparison for a limited amount of crack growth.     

DETERMINATIONS OF JIC FOR 2024-T351 ALUMINIUM ALLOY

Abstract— The J -integral is an elastic-plastic fracture mechanics parameter which can be regarded as a measure of the intensity of the crack tip stress and strain fields, irrespective of the plastic zone size. The value of J at the onset of stable crack extension, J _IC, has been suggested as a fracture criterion for both large-and small-scale yielding conditions. In this work the value of J _IC for an extruded, medium-strength aluminium alloy, 2024-T351 bar, was determined using; (i) the Hutchinson-Rice-Rosengren crack tip model and experimentally-determined crack tip strain profiles; and (ii) the ASTM standard multiple-specimen technique. Knowing the critical load for initial crack extension from the crack tip strain profile method also enabled J _IC to be computed using a finite element-hybrid contour method and a modified linear elastic fracture mechanics approach. Agreement between the J _IC values obtained by the various methods was good.     

PREDICTING THE EFFECTS OF CRACK TIP CONSTRAINT ON MATERIAL RESISTANCE CURVES USING DUCTILE DAMAGE THEORY

Abstract— In recent years much interest has been focused on the geometry dependence of the resistance to stable ductile crack growth of engineering materials, and in particular, in explaining this in terms of "constraint" effects. This paper describes the results of work using the Rousselier ductile damage model in finite element studies to simulate the growth and coalescence of voids, and hence the mechanics of ductile crack growth, to predict the effect of constraint on resistance to fracture. Using the modified boundary layer solution, where constraint is controlled by the application of remote displacements, it was possible to simulate resistance curves for different constraint conditions. This has produced a "net" of resistance curves, within which the curve for any specimen geometry can be found from a knowledge of the crack tip constraint for that specimen. This has been tested by comparing the results with those obtained from two specimens for which the constraint conditions are known. Good agreement has been achieved.
The results show that, although constraint has very little effect on conditions at the crack tip at initiation of crack growth, beyond that constraint plays an important part in defining the resistance curve. For low constraint geometries there is a very large loss in crack tip constraint which results in a large increase in the slope of the resistance curve. On the other hand, high constraint geometries exhibit very little dependence on crack tip constraint.