Load Bearing Research Articles

Effect of Different Static Load Test Methods on the Performance of Combined Post-Grouted Piles: A Case Study in the Dongting Lake Area

To investigate the effect of combined end-and-shaft post-grouting on the vertical load-bearing performance of bridge-bored piles in the Dongting Lake area of Hunan, two post-grouted piles were subjected to bi-directional O-cell and top-down load tests before and after combined end-and-shaft grouting, based on the Wushi to Yiyang Expressway project. A comparative analysis was conducted on the bearing capacity, deformation characteristics, and load transfer behavior of the piles before and after grouting. This study also examined the conversion coefficient γ values of different soil layers obtained from the bi-directional O-cell test for bearing capacity calculations. Additionally, the characteristic values of the end bearing capacity, obtained from the bi-directional O-cell and top-down load tests, were compared with the values calculated using the relevant formulas in the current standards, which validated the accuracy of existing regulations and traditional loading methods. The results indicate that the stress distribution along the pile shaft differed between the two test methods. In the bi-directional O-cell test, the side resistance developed from the end to the head, while in the top-down load test, it developed from the head to the end. After combined post-grouting, the ultimate bearing capacity of the piles significantly increased, with side resistance increasing by up to 81.03% and end resistance by up to 105.66%. The conversion coefficients for the side resistance in silty sand and gravel before and after grouting are 0.86 and 0.80 and 0.81 and 0.69, respectively. The characteristic values of the end bearing capacity, as measured by the bi-directional O-cell and top-down load tests, were substantially higher than those calculated using the current highway bridge and culvert standards, showing increases of 133.63% and 86.15%, respectively. These findings suggest that the current standard formulas are overly conservative. Additionally, the measured values from the top-down load test may underestimate the actual bearing capacity of piles in engineering projects. Therefore, it is recommended that future pile foundation designs incorporate both bi-directional O-cell testing and combined post-grouting techniques to optimize design solutions.

Analysis of reticulated dome with universal connector

In order to investigate the stress-strain state of a 4 m diameter reticulated dome model, four series of glued wooden rods were prepared for centric and eccentric compression tests. The tests were carried out in the laboratory of the Department of Metal Wood and Plastic Structures. The stresses at the specific points of the elements were determined through the deformations using the strain gauges. The feature of the prismatic specimens was the stress concentrators in the bearing areas in the form of holes for the arrangement of universal connectors. These areas were also reinforced with steel sleeves. The general conclusion of the study is the high load bearing capacity of the tested samples. The destruction of the samples occurred in the bearing zone due to wood crushing. The next research tasks will be to optimise the dimensions of the elements and test the dome model. The cross-section of the elements, in addition to providing the load-bearing capacity, is also influenced by the need to obtain certain thermal characteristics of the enclosure, i.e. the dome elements should have dimensions that allow placing a layer of an effective insulation in their plane. A special task is to choose a roofing that can be considered only as a part of the constant load on the load-bearing system or as a continuous shell that unbinds the frame.

Skin adaptation in lower limb amputees assessed through Raman spectroscopy and mechanical characterization.

Following lower limb amputation residuum skin from the lower leg is used to reconstruct the residual limb. Unlike skin on the sole of the foot (plantar skin), leg skin is not inherently load bearing. Despite this, leg skin is required to be load bearing in the prosthetic socket. Current hypotheses propose that lower limb amputee skin can adapt to become load bearing with repeated prosthesis use. Here, we show using confocal Raman spectroscopy, mechanical characterization and cytokine analysis that adaptations occur which actually result in impaired barrier function, higher baseline inflammation, increased coefficient of friction and reduced stiffness. Our results demonstrate that repeated frictional trauma does not confer beneficial adaptations in amputee skin. We hypothesize that non-plantar skin lacks the biological capabilities to respond positively to repeated mechanical trauma in the same manner observed in plantar skin. This finding highlights the need for improved therapies as opposed to current mechanical conditioning or product solutions that directly relate to improving load-bearing capacity on the skin of lower limb amputees. This study also highlights the importance of measuring multiple parameters of application-specific skin at different scales for skin tribology applications.

Data-driven prediction of high-temperature bond strength in corroded reinforced concrete

For accurately assessing the structural load bearing capacity of corroded reinforced concrete(CRC) structures after exposure to high temperatures, such as in sudden fire accidents, there is an urgent need for a unified model to predict the bond strength of CRC under high-temperature conditions. However, the degradation mechanism of bond strength in CRC under high-temperature conditions is highly complicated. Traditional empirical models cannot account for the multivariate correlations among factors such as high temperature, corrosion, and material properties. Based on a large amount of existing experimental data, ML methods can effectively establish a regression relationship between input and output features through data analysis. This paper utilized five ML algorithms, namely ANN, SVM, DT, RF, and XGB, to establish an interpretable prediction method for the high-temperature bond strength of CRC. The model was trained and tested using 612 sets of experimental data on high-temperature CRC. The results show that the predictions of the ML model are in good agreement with the experimental results. Moreover, the calculation outcomes of the ML model were compared with those of three theoretical calculation formulas, and the ML model demonstrated clear advantages. Furthermore, to address the black-box issue inherent in ML algorithms, the SHAP method was employed to enhance the interpretability of the bond strength prediction process for high-temperature CRC. This model will provide a theoretical basis for accurately assessing the extent of damage to CRC buildings after exposure to high temperatures.

Mechanical compressive properties of TPU 3D printed with various parameters

Shape memory polymer (SMP) is a material that has the ability to recover its original shape from a temporary (deformed) shape by applying external stimuli. The smart scaffold based on SMP is used to enhance delivery, load bearing, and tissue defect filling. Therefore, specimens with the structure of the face-centered cubic were produced under various printing conditions to characterize their effects on the mechanical properties. Fused deposition modeling is utilized to construct the specimens of shape memory thermoplastic polyurethane (MM-3520). Printing parameters with different levels were used in specimen fabrication, including layer thicknesses of 0.1, 0.2, and 0.3 mm, printing temperatures of 210, 220, and 230 ° C, and printing speeds of 20, 30, and 40 mm/sec. We performed the microstructural analysis under a microscope to examine the impact of printing factors on lattice structures. Then there is the compression test, which evaluates mechanical properties such as linear elastic stiffness, collapse stress, plateau stiffness, and densification stress. Analyzing the microstructure of the printed specimens exhibits that the specimens with the highest printing temperature, the lowest printing speed, and a thinner printing layer have better layer adhesion and lower porosities. As well, figures and main effect plots revealed that the specimens printed with a layer height of 0.1mm, a printing temperature of 230 ° C, and a printing speed of 20 mm/s had compressive strengths of 0.6129±0.062, 0.6018±0.106, and 0.6082±0.078 MPa, respectively. These are the highest results in terms of strength compared to other levels of parameters.

Study on the looseness caused by local slip and load bearing capacity of threaded connections under transverse cyclic loading

Abstract Under transverse cyclic loading, slip will occur on the contact surfaces in a threaded connection, causing rotational loosening of the connection. It is necessary to detect and analyze the loosening behavior of threaded connections caused by slippage. In this article, a self-driven sensor based on the principles of triboelectric nanogenerators was used to measure the rotational slip of a tight threaded stud connection subjected to transverse cyclic loads. The finite element simulation was conducted on the contact slip in the stud connection in the experiment under transverse cyclic loading. It was found that local slip propagation with the increase of load cycles would cause no-constant-sticking-area slip on all thread surfaces and lead to loosening of the connection. Under a certain preload, only when the amplitude of the lateral cyclic load does not exceed a critical value, will the thread contact surface not experience local slip propagation. Therefore, a slip load coefficient was proposed for calculating the critical transverse cyclic load amplitude, and its influencing factors were discussed. This study provides a new approach for the anti-loosening design of threaded connections.

The Effectiveness of Nonwoven Kenaf Geotextile in Improving Load Bearing of Soft Soil

The Effectiveness of Nonwoven Kenaf Geotextile in Improving Load Bearing of Soft Soil

Design of nonlinear rubber vibration isolators with low resonant frequency and high load bearing capacity

Designing a rubber vibration isolator to simultaneously meet the requirements on both low-frequency vibration isolation and high load carrying capacity has always been a major challenge. To tackle this problem, in this paper, a design strategy capable of effectively balancing these two effects to guide the design of such isolators is proposed. The rubber isolator static and dynamic behavior prediction models suitable for engineering applications are first established, where Yeoh model is adopted for rubber strong nonlinear feature prediction. Experiments are carried out to determine the material constants in Yeoh model and dynamic-to-static ratio of the rubber material. Combing with Multi-Objective Genetic Algorithm, a design strategy is proposed. The conducted experiments demonstrate that based on the proposed numerical model and design procedure, rubber isolators with enough load bearing capability and low-frequency vibration isolation performance can be successfully designed.

A comparative study of mid- and long-term effectiveness of patellar resurfacing or non-resurfacing in primary total knee arthroplasty

To compare the mid- and long-term effectiveness of patellar resurfacing versus non-resurfacing in primary total knee arthroplasty (TKA). Twenty-six patients who underwent bilateral TKA between March 2013 and September 2015 were selected as the study subjects. One side was randomly chosen for patellar resurfacing (resurfacing group), and the other side was not (control group). There were 4 males and 22 females, the age ranged from 51 to 65 years, with an average of 59 years. According to Kellgren-Lawrence classification, there were 21 cases of grade Ⅳ and 5 cases of grade Ⅲ in both knees. There was no significant difference in the surgical side, and preoperative clinical and functional scores of the Knee Society Score (KSS), visual analogue scale (VAS) score, and the composition ratio of anterior knee pain localization points between the two groups ( P>0.05). The operation time, intraoperative blood loss, postoperative abnormal signs such as patellar clunk, feeling of constraint, patellar tendon weakness, crepitus, or snow-on-glass sensation, and the occurrence of complications were recorded and compared. Patient subjective evaluations included Forgotten Joint Score (FJS) and the degree of difficulty in high-level knee activities (including flexion with load bearing, going upstairs, going downstairs, squatting and standing up, kneeling, knee extension, and crossing legs for 7 items); KSS clinical/functional scores and VAS scores were used to evaluate the recovery of knee joint function, and the location of anterior knee pain was determined by a localization diagram. The operation time of the resurfacing group was significantly longer than that of the control group ( P<0.05), and there was no significant difference in intraoperative blood loss between the two groups ( P>0.05). All patients' incisions healed by first intention; the hospital stay ranged from 8 to 23 days, with an average of 12.6 days. All patients were followed up 9-11 years, with an average of 9.7 years. Except for 1 case who died of multiple organ failure due to internal diseases at 9 years after operation and 5 cases with incomplete radiological data, the rest 20 patients were assessed radiologically and found that 1 side of the knee joint in the control group had patellar dislocation; the remaining patients had no prosthetic failure (fracture, loosening, displacement, etc.), patellar fracture, patellar necrosis, patellar instability, patellar tendon rupture, prosthetic revision, etc. No patients had reoperations due to patellar-related complications or anterior knee pain in both knee joints. At 2 years postoperatively and at last follow-up, there was no significant difference in the incidence of abnormal signs such as patellar clunk, feeling of constraint, patellar tendon weakness, crepitus, or snow-on-glass sensation, the incidence of high-level knee activity difficulty, and the composition ratio of anterior knee pain localization between the two groups ( P>0.05). The KSS clinical scores, functional scores, and VAS scores of both groups significantly improved compared to preoperative ones ( P<0.05); there was no significant difference in the comparison between the two groups at the two time points postoperatively ( P>0.05). At 2 years postoperatively and at last follow-up, there was no significant difference in FJS scores between the two groups ( P>0.05). Patellar resurfacing or not has similar mid- and long-term effectiveness in primary TKA.

Ultimate load bearing of helical piles prediction and evaluation using machine learning-based algorithms

ABSTRACT This study aims to predict the Ultimate Load-Bearing (ULB) capacity of Helical Piles (HP) using six Machine Learning Algorithms (MLA) on an in situ-based 110 pile load tests including a wide range of pile properties: shaft diameters (73–406 mm), helix diameters (254–762 mm), helix spacing (300–1000 mm), number of helices (1–6), pile lengths (2.4–16 m), and helix thicknesses (6–12 mm). The measured axial ULB is analysed using the Brinch-Hansen 80% criterion and 5% criterion of the average diameter of the helices. Load-displacement curves were fitted using the Hyperbolic Function. MLA including Multi Linear Regression (MLR), K-Nearest Neighbors (KNN), Decision Tree (DT), Random Forest, eXtreme Gradient Boosting, and Support Vector Regression were optimised to grid search for hyperparameters like neighbour count, tree depth, learning rate, and kernel type. Input parameters were categorised into Geometric and Soil Properties packages. Results indicate that the DT algorithm excelled in pullout loading, KNN in compression loading, and MLR for Brinch-Hansen 80% criterion estimations. The input parameters related to the soil surrounding the pile helices have the most impact on the ULB prediction of HP. This study enhances HP foundation design by enabling data-driven decisions for optimal pile selection and configuration.

Recycled coarse aggregate concrete and its application in CFRP reinforced concrete beam

This paper deals with performance of concrete by using recycled coarse aggregate (RCA) to replace 30%, 50%, and 70% of natural coarse aggregate. Three concrete types were studied: Group A using RCA with 10% of silica fume (SF) addition by weight of cement, Group B using RCA with 30% of fly ash (FA) substitution by weight of cement, and the control concrete without RCA, SF, FA. Group A demonstrated a considerable improvement in compressive strength whereas group B exhibited a noticeable reduction, in comparison to the control concrete. Secondly, three reinforced concrete beams, representing three concrete types, strengthened with carbon fiber reinforced polymer (CFRP) sheet were tested under a three-point bending fixture. All the flexural parameters of the tested beam, including load bearing capacity, deflection capacity, stiffness, ductility, and crack patterns were evaluated and discussed. Finally, an analytical model was suggested to estimate moment and shear resistance of the beams.

Managing Low-Velocity Mandibular Gunshot Wounds: An Institutional Review and the "FLOSS" Severity Scoring System.

Management of mandibular ballistic trauma is poorly delineated, given the variable injury complexity. This study examines surgical outcomes and presents a novel scoring system to define and guide the management of low-velocity ballistic mandibular fractures. A retrospective chart review was performed from 2015 to 2022 to collect data on patients who suffered ballistic mandibular fractures. Computerized tomography facial bone scans were analyzed to determine a mandible severity scoring based on the following "F.L.OS.S." variables: fracture description (F), location of fracture (L), other surrounding fractures (OS), and soft tissue involvement (S). Sixty-six patients suffered handgun-related mandibular fractures and 54 underwent surgical intervention. The mean FLOSS score was 7.9 for all surgical patients and significantly differed between treatment groups (P = 0.011). Certain injury-specific variables were significantly associated with higher FLOSS scores including >2 areas of comminution along load bearing, bony gap >10mm, or intraoral involvement with soft tissue avulsion; however, the degree of displacement, bilateral involvement, or presence of concomitant fractures did not predict higher scores. The types of complications did not significantly vary for total FLOSS score or FLOSS subcategories; the only exception being, an association between bony gap (>10mm) and hardware exposure (P = 0.045). Overall surgical complication rate was 26.9% and presence significantly varied between surgical treatments (P = 0.019); specifically, nonunion was the only significant subcategory (P = 0.030). The FLOSS scoring system may be a useful adjunct in defining fracture characteristics that guide appropriate surgical intervention for low-velocity ballistic mandibular injuries.

Research on calculation of allowable radial load of silicon nitride full ceramic ball bearing

Research on calculation of allowable radial load of silicon nitride full ceramic ball bearing

Reinforcement Learning assisted LQR Tuning of a Load Bearing Robotic Arm

Reinforcement Learning assisted LQR Tuning of a Load Bearing Robotic Arm

Experimental Study on the High Temperature Performance of UHPCFST Stub Columns at Different Concrete Age

Fire is one of the serious incidents occurring in the construction phase of Ultra-High Performance Concrete filled steel tubes (UHPCFST) columns, which may cause damage to materials, delays to construction and risk to life. This paper investigates the high temperature performance of UHPCFST columns at different concrete age to simulate the occurrence of fire at construction phase. Axial compression experiments on 24 stub columns are conducted to investigate the effect of temperature levels, age of UHPC on the mechanical response of the UHPCFST columns at different construction stages. The findings reveal that the bearing capacity of the UHPCFST stub columns shows an increase and then a decrease with rising temperatures, and columns of earlier age exhibit a greater increase in fire-resistance bearing capacity. Notably, the load-bearing capacity at room temperature increase with the age of UHPC. At 300 ℃, a marginal increment in capacity correlating with age is observed, whereas at 700 ℃, there is a slight decline. Furthermore, the incorporation of coarse aggregate substantially contributes to the augmentation of load-bearing capabilities across diverse conditions. Meanwhile, a formula for calculating the load bearing capacity and equivalent stress-strain curve of UHPCFST stub columns under elevated temperature at different concrete ages is proposed and validated. This research is expected to provide valuable insights for assessing fire safety and reliability of UHPCFST structure in construction settings.

Fisher-Tippet Law Truncated Form for Loading Modeling of Machinery Structures

Introduction. Statistical data are used as a basis for assessing the reliability of engineering structures. However, incomplete data or inaccurate modeling of random variables may lead to an overestimation of reliability indicators. In practice, laws with infinitely decreasing or increasing distribution functions of an exponential family are usually used to model random variables characterizing the bearing capacity, load, and resource of engineering structures. To improve the accuracy of modeling of random variables, truncated forms of distribution laws are often used. These forms allow us to consider the random variable within a specified interval, excluding impossible values. Several studies have suggested using the Fisher-Tippett law with three parameters for modeling random variables related to the loading of engineering structures. The advantage of this law is that it limits the range of the random variable on the right side, but the left side of the distribution function decreases indefinitely, which is not ideal for load characteristics. To improve the accuracy of predicting random variables that characterize the load, it would be helpful to have a left-sided restriction using the Fisher-Tippett law. Currently, there are no descriptions of truncated forms of the distribution law in scientific literature. This article will explore the justification and development of a three-parameter truncated form of the Fisher-Tippett law and its use in calculation methods. The goal is to create a left-sided truncated version of the Fisher-Tippett distribution with three parameters to model random variables within a specific range.Materials and Methods. The article provides a detailed description of the history of the Fisher-Tippet law, including its three-parameter form, and justifies the need for obtaining its truncated form.Results. As a result of the research, a truncated form of the Fisher-Tippet three-parameter law in differential and integral forms was obtained and substantiated. The findings included graphs and calculations that demonstrated the normalization of a random variable within a given range.Discussion and Conclusion. The conclusion was drawn about the advantages and disadvantages of the truncated form of the Fisher-Tippet law. The possibility of its practical application in the schematization of random loading processes under operating conditions and testing of machine elements and structures to assess fatigue life and determine fatigue resistance characteristics was established. The direction of further research is related to the practical use of the truncated form, particularly with the need to develop a method for evaluating the parameters of the truncated distribution and verifying the consistency of the proposed model

The Influence of Building Materials and Electrical Parameter Variability on Electromagnetic Wave Propagation

The article presents an analysis of the influence of building materials on the propagation of an electromagnetic wave and the values of the electric field intensity. The topics of the analysis were two types of walls (partition and load bearing) built of different building materials. Different variants of walls were considered due to the building material used: concrete, aerated concrete, solid brick, clinker bricks, and three types of hollow bricks. The requirements for structures in terms of wall thickness were taken into account. The article, using concrete as an example, also describes the influence of changes in the electrical parameters of the building material on wave propagation and the values of the field. The results concerning the influence of complex materials, such as hollow bricks, on the non-uniform distribution of the electric field were also included. Due to the different percentage share of ceramic mass in hollow bricks, the article discusses its influence on the values of the field, taking into account the variability of conductivity. The analysis was performed using the Finite Difference Time Domain (FDTD) method. The results were compared with the analytical solution. The analysis, among others, showed that with the increase in the ceramic mass in bricks, the electric field values are higher but result in an uneven distribution of the field. Using the example of hollow bricks used to build load-bearing walls, it was observed that a small modification of the hollows practically does not affect the field intensity (the difference is approx. 2%). When planning the installation of wireless networks, the best solution is walls made of ceramics with a large number of hollows, where the ceramic mass constitutes only approx. 30%. A multivariate analysis allows for a better understanding of field phenomena inside single-family homes.

Numerical assessment on a hybrid axial throughflow cooling scheme applied to the thermal management of bump-type gas foil bearings

Axial throughflow cooling is a practical thermal management solution for gas foil bearings (GFBs) with ultrahigh rotational speeds and small bearing clearances. The present study conducted a numerical investigation to assess a hybrid axial-throughflow cooling design (both inner cooling flow passing through the hollow shaft and outer cooling flow passing through the rotor–stator gap) for a specific radial bump-type gas foil bearing using the fluid–solid coupled modelling methodology. First, the individual effects of each cooling flow (i.e., the outer cooling mode only and the inner cooling mode only) on the GFB thermal behaviours are directly compared under a fixed rotational speed of ω = 1 × 105 rpm with a preset eccentricity ratio of ε = 0.9. The outer cooling mode exhibited superior cooling efficiency compared with the inner cooling mode with the same cooling air usage, albeit at the cost of a significantly greater flow pressure drop. Second, the conjugate roles of the hybrid cooling flows on the GFB thermal behaviours are related to the total cooling air mass flow rate of mtotal = 10 kg/h. Nine flow distribution relationships were comparatively studied between the two cooling flows under the same preset static bearing load of F = 31 N, wherein the percentage of the outer cooling flow (mouter/mtotal) varied from 10 % to 90 %. The heat removal pathway of the outer cooling flow was found to be dominant. The outer cooling flow exhibited a heat removal proportion close to 60 % when its distribution percentage was 30 %. The results of a comprehensive performance evaluation that considered the peak temperature reduction and cooling air pressure drop suggest a favourable distribution percentage of the outer cooling flow in the range of 30–40 %.

Dual hetero-structured Ti composites by manipulating self-assembled powder embedded with nano-reinforcements

Traditional discontinuously micro-reinforced titanium matrix composites (DRTMCs) produced by casting or forging, are usually confronted with the strength-ductility trade-off dilemma. Their micro-scale reinforcements easily cause incompatible deformation and stress localization. Novel self-assembled composite powder embedding nano-reinforcements paired with additive manufacturing technology has great potential to address this dilemma. Here, we report a special dual-heterogeneous structure with micro-scale networks and grain size gradients. It bespoke exciting strength-ductility synergy and excellent uniform elongation surpassing the as-deposited Ti6Al4V alloy by 32 %, while manifesting a steadier strain hardening behavior. Primarily, alternating basal <a> and pyramidal <a> slips together with substantial pyramidal <c+a> slips induced by hetero-interfaces significantly improved the uniform deformation ability. Then geometrically necessary dislocation (GNDs) and long-range back stress induced by strain inhomogeneity remarkably enhanced the strain hardening ability. This work firstly determined the most preferred orientation relationship (OR) (58.91°/ [010]TiB) between TiBw and the adjoining α-Ti in as-deposited composites. These interfaces showed higher interface strength (16.42 GPa) than those with the most preferred OR of 0°/ [010]TiB in as-forged TMCs, making more contributions to promoting the load bearing capacity of TiBw. It provided scientific guidance for in-situ synthesizing heterogeneous structures with attractive mechanical properties in Ti composites.

The Influence of Process Parameters on Tensile Features of Vetiver Fiber Reinforced Polymer Matrix Composites

Due to their outstanding specific strength and modulus, fiber-reinforced polymer composites have long been influential in a range of applications. Composites made of thermoplastic and vetiver fiber (VF) offer an alternative to synthetic polymers that cause environmental contamination. The advantages of natural fibers (like banana, sisal, coir, jute, vetiver, flax, hemp, kenaf, etc.) over conventional reinforcing fibers (glass and carbon fiber) are their ease of procurement, renewability, non-corrosive nature, light density, biodegradability, high specific energy (strength of density ratio), and low cost. In place of costly chemical treatment of VF in polymer composites, VF length management has been offered as a low-cost and ecologically friendly alternative. In the current study, VF-reinforced low-density polyethylene (LDPE) composites were altered using the film process stacking method with the hot press compression molding technique using a variety of process parameters, including VF condition (untreated and sodium dodecyl sulfate (SDS) treatment), VF sizes (short VF &lt; 3 cm and long VF &gt; 3 cm), and VF percent (5, 10, and 15 wt%). The tensile modulus and modulus efficiency factor of the LDPE composite were studied in relation to the impacts of VF size, VF content, and SDS treatment. The results showed that a specific amount of tensile modulus and modulus efficiency factor was boosted by VF content up to 10 wt%, processing temperature up to 160oC, and SDS treatment during processing up to 5 hours due to an increase in load bearing and interfacial adhesion. The improvement in tensile modulus and its efficiency factor because of efficient load transfer is evidently attributable to long VF load transfers, which have had a favourable impact. The brittle nature of the fibers caused a loss in ductility.