Influences of some materials on J-estimation methods for pipes with circumferential surface cracks

The approximate calculation methods (SC.ENG1 and SC.ENG2) for the J-integral for pipes with circumferential surface cracks are discussed and three-dimensional elastic–plastic finite element models for circumferentially surface-cracked pipe are conducted to evaluate the accuracy of these methods for different pipe materials used in China. The numerical studies verify that the SC.ENG2 method provides more accurate estimates of J than SC.ENG1. Based on three-dimensional elastic–plastic fracture analysis, the distribution of the local J-integral along the front of a circumferential constant-depth internal surface crack is investigated and the influences of different pipe materials with different yield plateaux on J-integral values are discussed. The validity of SC.ENG1 and SC.ENG2 J-integral estimation methods for pipe steel materials with different yield plateaux used in China are examined in detail and the SC.ENG2 method is found to provide reasonable estimates of J for materials with yield plateaux.     

Evaluation of leak-before-break assessment methodology for pipes with a circumferential through-wall crack. Part II: J-integral estimation

Evaluation of the J-integral plays a central part in evaluation of the critical crack length for unstable fracture for piping systems. Simplified evaluation methods for the J-integral for a circumferential through-wall crack in pipes subjected to axial and bending loading or their combination is reviewed in this paper. Use of the LBB.ENG2 method and a similar approach based on the η-factor concept were found to result in significant underestimation of the J-integral for small and medium crack angles. On the other hand, the reference stress method based on the solutions for stress intensity factor and limit load recommended in the companion paper (Part I) provides solutions which agree well with the available non-linear finite-element solutions and can be utilized as a powerful tool for J-integral evaluation for arbitrary materials, not restricted to simple power-law hardening.     

Quantification of ductile crack growth in 18G2A steel at different constraint levels

A constraint theory in fracture mechanics is used to analyze the test data of 18G2A steels using single edge-notched bend (SENB) specimens with various crack depth to specimen width ratios (a/W). A bending correction factor is included in the two-parameter (J–A₂) asymptotic solution to improve the theoretical prediction of the stress field for deep cracks under large-scale yielding condition, where J is the J-integral and A₂ is the constraint parameter, which depends on the in-plane geometry of the cracked body (a/W). As a result, the valid region for a traditional J-controlled crack growth is extended, and the ASTM specimen size requirements for fracture toughness testing can be relaxed. In addition, it is shown that the functional dependence of J–R curves on A₂ for 18G2A steels is established with test data; and the predicted J–R curves agree very well with the experimental curves. This ensures the transferability of laboratory test data to an actual structure provided the constraint level (A₂) of the cracked structure is known or determined. This procedure allows an appropriate J–R curve with the same constraint level to be constructed and used in flaw stability analysis of any cracked body.     

Limit load and J estimates of a centre cracked plate with an asymmetric crack in a mismatched weld

The limit load and J estimates of a centre cracked plate with an asymmetric crack in the tensile properties mismatched weld were investigated. A limit load expression was derived on the basis of a simplified slip-line field. A good agreement between the predictions of the expression and finite element (FE) results was found for ratios of half-weld width to the crack ligament, H/l, of less than 0.5. The equivalent stress–strain relationship method (ESSRM) was used to predict elastic–plastic J values. Results from FE analyses show that the ESSRM is accurate for the crack with asymmetry in the mismatched weld provided an accurate theoretical or numerical value of the limit load of the same specimen is available. Defect assessment methods are discussed, and it is found that the failure assessment diagram (FAD) of an asymmetrically cracked mismatched weld can be constructed from the equivalent stress–strain relationship for the same mismatched geometry with a symmetric crack. The effect of an asymmetric crack on the FAD may then be covered by the limit load solution for the asymmetrically cracked mismatched weld.     

Evaluation on over photocurrents measured from unmasked dye-sensitized solar cells

We have investigated the change in photocurrent density (J_SC) of dye-sensitized solar cell (DSSC) before and after covering an aperture mask on the cell, especially its dependence on solar absorption range in dye. Four different dyes having absorption threshold at 460 nm (P5), 520 nm (TA-St-CA), 680 nm (N719) and 820 nm (N749) are tested. J_SC of the DSSC without mask decreases after mask, where the decreasing rate (△J_SC = J_SC (no mask) − J_SC (with mask)/J_SC (no mask)) becomes larger when dye absorption threshold decreases. △J_SC at the given TiO₂ film thickness of 10 μm is determined to be about 20%, 15% and 13% for P5, TA-St-CA and N719-N749, respectively, which is reduced to 14% (TA-St-CA), 11.3% (N719) and 10.5% (N749) after increasing the thickness to 20 μm, except for P5 dye remaining unchanged. According to the analysis based on IPCE and photon flux data, the over photocurrents observed for the unmasked dye-sensitized solar cells and their dependence on dye absorption range are found to be attributed to diffuse light leaving the dye-adsorbed TiO₂ active area.     

Derivation of ‘γ’ parameter from limit load expression of cracked component to evaluate J–R curve

Experimental evaluation of the J-integral requires the ‘η_pl’ function, proposed by Rice et al. [Progress in flaw growth and fracture toughness testing (1973) 231], to multiply the area under the load vs. plastic load-line-displacement curve. However, the J-integral, thus evaluated, requires modification if crack growth occurs. A ‘γ’ term was proposed by Hutchinson and Paris [Elastic–plastic fracture (1979) 37] and later generalised by Ernst et al. [Fracture mechanics (1979) 581] and Ernst and Paris [Techniques of analysis of load–displacement records by J-integral methods (1980)] to correct the J-integral to account for crack growth. The η_pl and γ functions are available for very few geometries under specific loading conditions. A limit load-based general expression of η_pl was given by Roos et al. [Int J Pres Ves Piping 23 (1986) 81], but no such expression is available for γ functions. The advantage of having limit load-based general expressions for η_pl and γ functions is that the limit load for a particular geometry subjected to a specific loading condition is easily available in the open literature. In the present paper, a limit load-based general expression for the γ function is derived. The general expression is then validated by deriving the known γ functions of various geometries subjected to various loading conditions, which are available in the open literature. The general expressions are then used to derive new η_pl and γ functions for same pipe and elbow geometries with various crack configurations under different loading conditions, for which no solutions are available in the open literature. Finally, experiments have been carried out on 200 mm nominal bore (NB) elbows with throughwall circumferential cracks under in-plane bending moment. The proposed new expressions of η_pl and γ functions for this geometry are used to obtain the J–R curve from the experimental load vs. load-line-displacement and load vs. crack growth data.     

An explicit J-V model of a solar cell for simple fill factor calculation

The J-V equation of a solar cell is implicit and requires iterative calculation to determine the fill factor and the maximum power point. Here an explicit model for J-V characteristic is proposed which is applicable to a large variety of solar cell. This model allows an easy estimation of fill factor from four simple measurements of the bias points corresponding to V_oc, J_sc, and any two voltage values lying between 0 and V_oc, where V_oc is the open circuit voltage and J_sc is the short circuit current density.     

Local investigation of hot spot areas on multicrystalline silicon solar cells

The formation mechanism and the electrical consequences of hot spots have been investigated in multicrystalline solar cells. The hot spots were revealed by means of an IR camera when the cells are reverse biased in the dark. The minority carrier diffusion length (L_n), the open-circuit photovoltage (V_oc) and the short-circuit photocurrent (J_sc) were measured both in the hot spot area and far from this zone by masking off and etching small mesa diodes around suspect areas. Dark forward I–V curves were plotted in order to compute the values of ideality factor (M) and reverse saturation current (J_o).It is found that J_o and M are higher in the hot spot area, while J_sc, V_oc and, to a less extent, L_n are smaller. Large densities of dislocations and lineages structures are revealed in the abnormally heated region by chemical etching of the samples. The dislocations involved in the hot spot formation could act as shunting paths for leakage currents, in addition to their contribution to recombination-generation currents.     

Elastic–plastic J and COD estimates for axial through-wall cracked pipes

This paper proposes engineering estimation equations of elastic–plastic J and crack opening displacement (COD) for axial through-wall cracked pipes under internal pressure. On the basis of detailed 3D finite element (FE) results using deformation plasticity, the plastic influence functions for fully plastic J and COD solutions are tabulated as a function of the mean radius-to-thickness ratio, the normalised crack length, and the strain hardening. On the basis of these results, the GE/EPRI-type J and COD estimation equations are proposed and validated against 3D FE results based on deformation plasticity. For more general application to general stress–strain laws or to complex loading, the developed GE/EPRI-type solutions are re-formulated based on the reference stress (RS) concept. Such a re-formulation provides simpler equations for J and COD, which are then further extended to combined internal pressure and bending. The proposed RS based J and COD estimation equations are compared with elastic–plastic 3D FE results using actual stress–strain data for Type 316 stainless steels. The FE results for both internal pressure cases and combined internal pressure and bending cases compare very well with the proposed J and COD estimates.     

Relevance of plastic limit loads to reference stress approach for surface cracked cylinder problems

To investigate the relevance of the definition of the reference stress to estimate J and C* for surface crack problems, this paper compares finite element (FE) J and C* results for surface cracked pipes with those estimated according to the reference stress approach using various definitions of the reference stress. Pipes with part circumferential inner surface cracks and finite internal axial cracks are considered, subject to internal pressure and global bending. The crack depth and aspect ratio are systematically varied. The reference stress is defined in four different ways using (i) a local limit load, (ii) a global limit load, (iii) a global limit load determined from the FE limit analysis, and (iv) the optimised reference load. It is found that the reference stress based on a local limit load gives overall excessively conservative estimates of J and C*. Use of a global limit load clearly reduces the conservatism, compared to that of a local limit load, although it can sometimes provide non-conservative estimates of J and C*. The use of the FE global limit load gives overall non-conservative estimates of J and C*. The reference stress based on the optimised reference load gives overall accurate estimates of J and C*, compared to other definitions of the reference stress. Based on the present findings, general guidance on the choice of the reference stress for surface crack problems is given.     

An analysis of the numerical path dependence of the J-integral

Path dependent behaviour of the J-integral computed from the results of a finite element analysis may have two sources. The first is the history dependence of the strain energy, which causes J to lose its crack tip strain field characterizing property. The second is rooted in the principle of the finite element displacement method which ensures equilibrium only for each element as a whole, not for points within an element. It is of the utmost importance for a J-based safety assessment that these two sources be clearly distinguished as the latter may be reduced by mesh refinement whereas the former may serve as a criterion for assessing whether J can still be interpreted in its crack tip characterizing sense.The present paper proposes a numerical procedure for this distinction. Two examples confirm the procedure's validity and illustrate the practical necessity of careful evaluation of computed J-values.     

Material characterization by J-R curves of a 20MnMoNi55 forging

J-R curves have been determined for one specific forging of the reactor pressure vessel steel 20MnMoNi55 to characterize its fracture resistance in the upper shelf toughness regime. The multiple specimen unloading (MSU), a direct current potential drop (DCPD), and the single specimen partial unloading compliance (SSPUC) methods have been applied to test different CT-specimen geometries at temperatures between 25 and 300°C.The J–R curves are temperature dependent showing a minimum of slope and absolute values at 200°C. The critical J-values for onset of stable crack growth in the scatter of the results are independent of temperature and geometry: J_i ≈ 180 kJ/m². The values of the technical initiation toughness J_IC according to ASTM E813⁷ and according to Loss et al. (1979),⁸ the tearing modulus T, and the instability parameter J₅₀ show corresponding temperature trends as the J-R curves with a minimum at about 200°C.The material data have been used to evaluate the ductile failure initiation and tearing instability of several structural tests. The quality of agreement between calculable predictions and experiments is shown to depend on the input material J-R curve and evaluation of the loading which requires detailed knowledge about the material stress-strain behaviour and the relevant crack tip constraint.     

Use of local and global limit load solutions for plates with surface cracks under tension

Some available experimental results for the ductile failure of plates with surface cracks under tension are reviewed. The response of crack driving force, J, and the ligament strain near the local and global limit loads are investigated by performing elastic-perfectly plastic finite element (FE) analysis of a plate with a semi-elliptical crack under tension. The results show that a ligament may survive until the global collapse load is reached when the average ligament strain at the global collapse load, which depends on the uniaxial strain corresponding to the flow stress of the material and the crack geometry, is less than the true fracture strain of the material obtained from uniaxial tension tests. The FE analysis shows that ligament yielding corresponding to the local limit load has little effect on J and the average ligament strain, whereas approach to global collapse corresponds to a sharp increase in both J and the average ligament strain. The prediction of the FE value of J using the reference stress method shows that the global limit load is more relevant to J-estimation than the local one.     

Management of oil producing Jatropha curcas silvopastoral systems: Risk of herbivory by indigenous goats and competition with planted pastures

There is potential for Jatropha curcas production in South Africa especially in silvopastoral systems where the co-occurrence of oil production and grazing results in the optimal use of increasingly limited land. However, in South Africa there is a moratorium on J. curcas cultivation due to insufficient information on this species. The aim of this study was to assess the potential growth and suitability of J. curcas in silvopastoral systems. For such systems to succeed there needs to be limited competition between J. curcas and the forage component and the former must not be at risk to defoliation by livestock. The effect on the growth of 15-month old J. curcas trees by neighbouring forage species was addressed by removing planted pastures at 0, 60, 120 and 300 cm from the base of J. curcas individuals. Final height, basal diameter and percentage leaf abscission of trees with pasture removed up to 60 and 120 cm away did not differ significantly from treatments with the greatest and least amount of competition. Therefore, removing up to 60 cm will allow for growth similar to that of trees with 300 cm of pastures removal while still providing sufficient pasture for grazing. The palatability of J. curcas was determined through two two–choice and three-choice trials. Since goats spent <3.77% of their time browsing J. curcas it is a suitable candidate for silvopastoral systems provided that surrounding vegetation is removed at a recommended distance of 60 cm from the base of the tree.     

Improvement of polymer/fullerene solar cells by controlling geometry of the ITO substrate surface

We have found that the short-circuit current, J_sc, of polymer/fullerene [RR-P3HT/C₆₀] solar cells has a clear dependence on the surface roughness of the ITO/glass substrate. We prepared an ITO surface with an average roughness, R_a, of 0.7–11 nm by chemical etching. At first J_sc increases with the increase in ITO surface roughness and then gradually decreases. The maximum performance was obtained at R_a≈4 nm. J_sc is also high with a very flat surface of R_a=0.7 nm. This feature can be attributed to the trade-off between the increase in absorption light path length and film-quality deterioration.     

Analytical derivation of explicit J–V model of a solar cell from physics based implicit model

Recently a simple explicit model was introduced to represent the J–V characteristics of an illuminated solar cell with parasitic resistances and bias dependent photocurrent as v^m + jⁿ = 1. Here the normalized voltage, v and normalized current density j can be represented as v = V/V_oc and j = J/J_sc respectively, where V_oc is the open circuit voltage and J_sc is the short circuit current density. This model is useful for design, characterization and simple fill factor calculation and its applicability was demonstrated with the measured data of a wide variety of solar cells. This explicit form is intuitive and hence the model lacks the analytical support. In this paper an analytical derivation of this closed form explicit model is presented, which is derived from the physics based implicit J–V equation. The derivation expands the scope of model applicability and provides a new insight of analytical modeling of the solar cell.     

The effect of an elevated temperature aqueous environment upon the J-controlled tearing of a low-alloy steel

Monotonic rising-load J-integral tests were conducted on an ASTM A508-2 steel in both air and low-oxygen water environments at 243°C. The ASTM E1737 multiple-specimen method was employed in order to eliminate any concerns about corrosion–fatigue interactions that could arise in the unloading-compliance method. The onset of stable tearing, J_IC, was unaffected by the environment, but post-J_IC tearing in the water environment was characterized by “pop-in” events. It is postulated that the pop-in events may be associated with quasi-cleavage events near MnS inclusions and dynamic strain aging in the steel.     

Determination of the diode parameters of a-Si and CdTe solar modules using variation of the intensity of illumination: An application

An attempt has been made for the determination of diode parameters viz. shunt resistance R_sh, series resistance R_s, diode ideality factor n and reverse saturation current density J₀ of three solar modules: a-Si 47-37, a-Si 51-13 and CdTe 14407. In this regard, two approaches namely (A) and (B) reported by Khan et al. (2010) have been used to determine all the four diode parameters R_sh, R_s, n and J₀. The data of slopes of J-V curve at open circuit conditions (m_oc) and open circuit voltage (V_oc) at different illumination intensities obtained by Del Cueto (1998) for two a-Si and one CdTe solar modules have been used to determine the above diode parameters. The determined values of diode parameters have been used to generate the theoretical J-V curves. The theoretical fill factor (FF) and V_oc have been calculated from the theoretical J-V curves and are plotted along with the experimental FF and V_oc values. The theoretical values of FF and V_oc obtained by the approach (B) of method of Khan et al. (2010) are in good agreement with the experimental values.     

Nondestructive local analysis of current-voltage characteristics of solar cells by lock-in thermography

By evaluating dark lock-in thermography images taken at one reverse and three forward biases, images of all two-diode-parameters J₀₁, J₀₂, n (ideality factor of J₀₂), and G_p (the parallel Ohmic conductivity) of the dark current-voltage characteristic are obtained. A local series resistance is explicitly considered and may be provided as a series resistance image, e.g. resulting from luminescence imaging. The results enable a separate investigation of factors influencing the depletion region recombination current and the diffusion current, which is governed by the bulk lifetime. Local I-V characteristics of special sites may be simulated.     

The power law J-V model of an illuminated solar cell

We have earlier introduced the power law equation, j=1−(1−γ)v−γv^m, where j=J/J_sc and v=V/V_∝, to simplify determination of the J-V curve, fill-factor and peak power point of an illuminated solar cell from a few measurements as well as physical parameters. However, the validity of the various formulae and parameter extraction procedure was established for a limited class of cells, having moderately convex J-V curves with fill-factors of 0.56-0.77 and obeying single exponential theory with bias independent photocurrent. This paper presents a thorough validation of the model proposed earlier. New formulae and parameter extraction procedure are presented to extend the applicability of the power law equation to a much wider variety of cells. The J-V curves considered in this paper range from concave (fill-factor<0.25) to highly convex (fill-factor>0.85), and their theoretical expressions contain bias dependent photocurrent and double exponential terms. It is shown that the power law equation also simplifies the calculation of the cell bias point for an arbitrary load.