Scatter In Test Data Research Articles

Anchorage and lap capacity of plain surface and square twisted bars in existing R.C. Structures: A comprehensive approach

AbstractAlthough plain round or square section reinforcement is no longer used in new construction, there are many older structures still in service built with such bars. In recognition of the need for guidance on the assessment of load‐carrying capacity of structures reinforced with such bars, design codes are now introducing or re‐introducing provisions to assess the capacity of laps and anchorages of such reinforcement. The authors have contributed to the introduction of design rules in the fib Model Code 2020. This paper describes the derivation of these provisions. Starting from the form of expression proposed earlier by the authors, the data from which these proposals are derived is specified and modifications in interpretation preparatory to a statistical analysis are outlined. A rigorous multivariate statistical procedure is then employed firstly to determine a mean strength expression for the capacity of anchorages and laps which is then validated against test data. Further statistical analysis is subsequently used to determine a design expression using the approach outlined in EN 1990, taking appropriate account scatter in test data. Finally, some comparisons are presented between the assessment expressions proposed and design provisions that were in place when these types of bars were in common use. Areas where earlier design provisions may be non‐conservative are identified.

Robust Determination of Fatigue Crack Propagation Thresholds from Crack Growth Data.

The robust determination of the threshold against fatigue crack propagation is of paramount importance in fracture mechanics based fatigue assessment procedures. The standards ASTM E647 and ISO 12108 introduce operational definitions of based on the crack propagation rate and suggest linear fits of logarithmic – test data to calculate . Since these fits typically suffer from a poor representation of the actual curvature of the crack propagation curve, a method for evaluating using a nonlinear function is proposed. It is shown that the proposed method reduces the artificial conservativeness induced by the evaluation method as well as the susceptibility to scatter in test data and the influence of test data density.

Fatigue Life Testing of Locally Additive Manufactured AlSi10Mg Test Specimens

In order for additive manufacturing to become a viable manufacturing method for aerospace engineering, it is required that exhaustive static and fatigue testing be performed. The testing is required in order to describe material properties in a statistical manner. Fatigue tests were performed on standard additive manufactured ASTM E466 test specimens in order to obtain the low (1000 cycles) to high cycle (1E6 cycles) behaviour of AlSi10Mg. The specimens were manufactured using non-heat treated, but stress relieved specimens. Specimens were printed in three build directions, namely the XY (parallel with build plate), 45 degree and vertical direction as measured with respect to the build baseplate. The three different directions were chosen to investigate the sensitivity of the material properties to the build direction. The specimens were stress relieved on the baseplate. Static testing was also performed on specimens according to ASTM E8/E8M. The specimens were produced to have a surface finish representative of standard deburring techniques used in the aerospace industry. The surface roughness on the specimens were measured. The scatter in test data as a result of the surface finish on material properties is quantified. It is a requirement to quantify the effect of the surface roughness on fatigue failure allowable values since a machined type finish (less than 3.2 micrometer) is not always practically possible to achieve with additive manufactured structures. This is because the organic shapes produced with additive manufacturing makes some surfaces inaccessible to normal surface finishing techniques. Furthermore, some internal structures such as lattice structures are completely inaccessible to surface finishing techniques such as polishing or lapping. In addition to the surface roughness the roundness of the test section was also measured using inspection equipment. This was required since the industrial deburring techniques did not yield a completely concentric test section as a lathe operation would produce. Once again this is representative of an additive manufactured structure. The fatigue tests were performed at an R-ratio of 0.1. The test results were used to produce Wöhler or S-N curves for the material in all three material directions. The scatter was quantified using industry accepted methods. The results were compared with fatigue test results from literature of specimens produced with a lathe in order to compare a practical industrial surface finish on an additive manufactured component with a machined surface finish. It was found that the build support structures of the additive manufacturing process causes stress concentrations in the fatigue test specimens. This leads to a reduction in fatigue life and an increase in the scatter of the results.

Site characterization with multiple measurement profiles from different tests: A Bayesian approach

Uncertainty studies and reliability assessments have become important topics/areas in geotechnical engineering, and different site-characterization approaches have been developed in an attempt to incorporate the sources of uncertainty into the analysis. Focusing on a target problem with multiple measurement profiles (with depth) from different testing procedures, this paper presents a site-characterization modeling to estimate the probability distribution of soil properties for a given site, considering the uncertainties from site-specific test-data scatter and from inherent soil variability in space (or in horizontal direction). More specifically, the modeling adopts the Bayesian approach to integrate the multiple sources of data, by using one as prior and the other as the so-called likelihood function. In addition to the algorithms, the approach was applied to a site with two sources of undrained shear strength from laboratory triaxial tests and in-situ plate bearing tests, and suggested a series of characteristic values for undrained shear strength for the site, corresponding to a given depth of interest, and to a given level of inherent soil variability in the horizontal direction.

Ligament rupture and unstable burst behaviors of axial flaws in steam generator U-bends

Incidents of U-bend cracking in steam generator (SG) tubes have been reported, some of which have led to tube rupture. Experimental and analytical modeling efforts to determine the failure criteria of flawed SG U-bends are limited. To evaluate structural integrity of flawed U-bends, ligament rupture and unstable burst pressure tests were conducted on 57 and 152mm bend radius U-bends with axial electrical discharge machining notches. In general, the ligament rupture and burst pressures of the U-bends were higher than those of straight tubes with similar notches. To quantitatively address the test data scatter issue, probabilistic models were introduced. All ligament rupture and burst pressures of U-bends were bounded by 90% lower limits of the probabilistic models for straight tubes. It was concluded that the prediction models for straight tubes could be applied to U-bends to conservatively evaluate the ligament rupture and burst pressures of U-bends with axial flaws.

A modified constitutive equation for elevated temperature flow behavior of Ti–6Al–4V alloy based on double multiple nonlinear regression

Constitutive analysis for hot working of Ti–6Al–4V alloy was carried out utilizing experimental stress–strain data from isothermal hot compression tests, in a wide range of temperatures (1073–1323K), strains (0.1–0.5) and strain rates (0.0005–1s−1). A modified constitutive equation based on multiple nonlinear regression (DMNR) has been established considering the independent effects of strain, strain rate, temperature and their interrelation. A comparative study has been made on the capability of strain-compensated Arrhenius-type Constitutive Model (SACM), orthogonal experiment and Variance Analysis Constitutive Model (OVCM) and DMNR model. Suitability of these models was evaluated by comparing the correlation coefficient, average absolute relative error and statistical analysis. It is observed that the OVCM is not suitable in providing good description of flow behavior of Ti–6Al–4V alloy in the above hot working domain. Predictions of the other two models are in close agreement with the experimental data. However, the DMNR model was based on the test data scatter plot which did not need a specific constitutive form in advance and had a lower standard deviation. It indicates that the developed constitutive equation considering the coupling effects among strain, strain rate and deformation temperature can predict flow stress of Ti–6Al–4V alloy with good correlation and generalization.

Fatigue Evaluation of Rib-to-Deck Welded Joints of Orthotropic Steel Bridge Deck

This study reported fatigue test results of 300-mm-wide specimens with three details: 80% partial joint penetration (80%PJP), weld melt-through (WMT), and both. The specimens were cut out from full-scale orthotropic deck specimens of 16-mm-thick deck plate. In the fatigue test, the deck plate was subjected to cyclic bending loading and the rib was free from loading. The fatigue fracture surfaces showed that the presence of WMT may affect the initiation of fatigue cracks. A propensity to root cracking rather than toe cracking was observed. Plotting fatigue test results in an S-N diagram showed that the specimens with WMT seemed to have slightly lower fatigue strengths than the 80%PJP specimens, but the difference is more likely to be within a usual scatter of test data, which means that both details have comparable fatigue strength. The present test results satisfied the S-N curves of JSSC-E (80 MPa at 2×106 cycles) or AASHTO-C (89 MPa at 2×106 cycles).

Cyclic deformation behaviour and fatigue crack propagation in AZ91HP and AM50HP

The purpose of the present work was to investigate room temperature cyclic deformation and crack propagation behaviour in the most widely used die casting magnesium alloy AZ91HP with different heat treatments. In addition, examination of the low cycle fatigue properties of solid solution treated alloy AZ91HP-T4 was emphasised in comparison with AM50HP. Obvious cyclic strain hardening was found in low cycle fatigue tests, especially for AZ91HP-T4 at high cyclic strain amplitudes. Nevertheless, it was very difficult to evaluate differences in low cycle fatigue behaviour between die casting alloy AZ91HP-F, artificially aged alloy AZ91HP-T6, solution treated alloy AZ91HP-T4, and AM50HP(-F) because of the scatter of test data. However, it may be concluded that the last two alloys had greater plastic strain components during cyclic deformation, and AZ91HP-T4 exhibited a longer fatigue life than that of AM50HP at the highest strain amplitude. According to results of tests carried out on AZ91HP compact tension (CT) specimens, it was concluded that solution treatment could reduce the fatigue crack propagation rate, and plasticity induced crack closure was considered to have a predominant effect on fatigue crack propagation.

A paraboloid failure surface for transversely isotropic materials

An invariant 3-D failure criterion for transversely isotropic solids is presented. For isotropic conditions, this criterion reduces to Mises–Schleicher failure criterion. It is shown that the anisotropic Mises–Schleicher (AMS) criterion can accurately describe the observed failure characteristics of transversely isotropic rocks under both compressive and tensile stresses. This criterion predicts that the application of multiaxial tensile stresses on rock reduces the value of the failure strength, i.e., the predicted value of the hydrostatic tensile strength as well as of the biaxial tensile strength is less than the uniaxial tensile strength in any direction. The intersections of the AMS failure surfaces with the octahedral plane demonstrates the ability of the criterion to describe the directional character of the strength of transversely isotropic materials under general loading conditions. The application of this criterion to conventional triaxial compression, reduced triaxial extension, and biaxial conditions, shows that this criterion captures the influence of the magnitude of the intermediate principal stress on strength. Representative sets of data from tests on rock have been analyzed and comparison between the theoretical predictions and the data appears to be quite good with the accuracies generally within the natural scatter of test data. In this paper, the AMS criterion is applied to rock materials; however, it can be used to describe the strength anisotropy of any material exhibiting transverse isotropy.

EXPERIMENT AND ANALYSISON THE RESPONSE OF CURVED LAMINATED COMPOSITE PANELS SUBJECTED TO LOW VELOCITY IMPACT

Transverse central impact on thin fiber-reinforced composite cylindrical panels is studied with emphasis on the importance of in-plane membrane effects. Both small and large deformation impact responses are examined in this context. A nonlinear system of equations is derived for the impact problem, including Hertz’ contact law, and solved over time using Runge–Kutta integration. Drop weight impact tests were performed to validate the analyses. Impact force and displacement histories are compared with the test data and the work of other researchers for small and large deformation of flat and curved panels. Understanding the scatter of test data and limits on the assumptions enables both quantitative and qualitative examination of the parameters which govern the impact response.

A New Method of Correcting Unconfined Compressive Strength of Natural Clays for Sample Disturbance

ABSTRACT In Japan, the unconfined compression test is used widely to determine undrained strength for natural clays. The scatter of test data caused by sample disturbance, however, prevents this test from being used effectively and economically in geotechnical engineering practice. This paper is aimed at proposing a simple rational approach to correct the unconfined compressive strength, qu, of natural clays for sample disturbance. The effect of sample disturbance on qu is analyzed both qualitatively and quantitatively based on the experimental data for five types of natural clay. The results indicate that qu normalized by the corrected yield stress, pyf, decreases linearly with the increase of the defined degree of sample disturbance. The straight line representing the relationship between the reduction value of qu/pyf the disturbance degree is determined by regression analysis. The slope of the linear regression line is defined as a strength correction coefficient. Based on such correction coefficient, a simple method is proposed in this paper for correcting qu for sample disturbance. The problem of scattered test data on qu can be eliminated with the proposed method. Analyses and comparisons are also made of the experimental data on unconfined compression tests and triaxial consolidated undrained shear tests for some natural clays as well as the data published in the literature. The results indicate that the proposed method is valid for natural clays.

A cumulative damage theory for creep and creep-fatigue interaction

A cumulative damage theory is developed based on the concept of bounds on residual life. Previous results applicable to fatigue are generalized to creep-rupture and to creep-fatigue interaction. By defining a creep endurance limit and void-initiation life fractions, a complete symmetry is established between the creep and fatigue cumulative damage problems. This enables the derivation of bounds for two-stage creep exposures as well as for creep-fatigue and fatigue-creep interactions. The question of test data scatter in cumulative damage tests is considered, and optimum bounds are derived which bracket the entire test data scatter.

A cumulative damage theory for fatigue life prediction

A cumulative damage theory is developed based on the concept of bounds on residual fatigue life in two-stage cycling. It is shown that such bounds follow from general properties of damage curves and involve only fatigue lifetimes and the endurance limit in single-stage cycling. It is then shown that such bounds can be narrowed by inclusion of additional information about the fatigue process, namely, crack-initiation and crack propagation lifetimes. The question of scatter in cumulative damage tests is considered and it is shown that the bounds can be optimized to bracket the entire test data scatter. As a result, it is found that the scatter in crack initiation cycles underlies the scatter observed in cumulative damage tests.

Probabilistic Analysis Of Offshore Site Exploration

The uncertainties associated with the predicted bearing capacity of an offshore gravity platform arise from incomplete knowledge about the type of material that is encountered at different points along the slip surface and the strengths of these materials. Uncertainty about material strength is caused by scatter in test data and differences between measured strength and in-situ strength. The probability of finding indifferent materials, given the materials as identified at the location of boreholes, is evaluated from the proximity rule. This is combined with the uncertainty due to data scatter and inaccuracy of the test methods to estimate the variance of the foundation resistance. The procedure makes is possible to evaluate the uncertainty about foundation resistance at various stages of a site exploration program. The effects of additional boreholes and improved testing methods can be evaluated separately and used to help decision making in site exploration. The site exploration data from the Brent B-G site are analyzed as an example.

Diffusion bonding and testing of Al-alloy lap shear test pieces

A quantitative measure of the effect of processing variables on the shear strength of solid state diffusion bonds is often difficult to obtain because of the scatter in test data. This may be reduced by improving the bonding and testing techniques. Two jigs for bonding and testing small Al-alloy lap shear test pieces are described. These jigs enabled the precise measurement of shear stress-strain curves for lap joints and led to reproducible shear strength values. Results obtained for diffusion bonded lap joints between clad Al-Zn-Mg (7010) alloy are described.

Stability of deep cuts in soft estuarine clays : Bell, R A; Theissen, J R; Tsai, K W Proc 10th International Conference on Soil Mechanics and Foundation Engineering, Stockholm, 15–19 June 1981V3, P353–356. Publ Rotterdam: A. A. Balkema, 1981

Increased development of reclaimed tidal marshland will require deeper excavations than previously attempted in such soils. This paper describes analysis to design stable slopes for an 8,5 M deep excavation in San Francisco bay mud. Published strength correction factors and observed strength variations due to testing procedures, topographic features and construction activities were incorporated in analysis to improve predictions. Based on the results of these studies it is concluded: (1) seemingly insignificant strength reductions (within the scatter of test data) caused by such topographic features as former sloughs or construction traffic may influence stability of planned slopes, (2) use of percentage strength correction factors on bay mud soils may underestimate soil strengths at depth due to inappropriate reduction of the ratio, (3) small diameter laboratory van shears tests of bay mud soils may overestimate actual strengths by approximately 45 per cent, (4) lower bound test results may provide a reasonable first approximation of actual in situ strengths of bay mud soils, provided sufficient data exist to yield a representative strength envelope. (TRRL)

Hydrostatic and Axial Collapse Tests of Stiffened Cylinders

This paper describes the results of collapse tests on two models of longitudinally and circumferentially stiffened leg sections of an offshore platform. Methods of predicting buckling loads are discussed and predicted platform. Methods of predicting buckling loads are discussed and predicted buckling loads are compared with the model test results. Introduction Structural elements can collapse because of material failure or geometric buckling. Cylindrical shells of low diameter-to-thickness ratios (d/h less than 60), such as tabular members of conventional offshore platforms, generally do not buckle locally and can be designed on the basis of Euler column buckling or material failure. Cylindrical shells of relatively high ratios (d/h greater than 60), on the other hand, may be subject to local shell buckling. Unstiffened thin-walled cylinders are prone to sudden and disastrous failures at loads well below buckling loads predicted by classical small-deflection theory. The predicted by classical small-deflection theory. The behavior of unstiffened cylinders is especially unpredictable when they are subjected to axial compression and bending loads. In fact, the scatter of test data may range up to 500 percent or more. Donnell and Wan showed theoretically, by means of an imperfection analysis, that a possible reason for the discrepancy was initial imperfections caused by manufacturing tolerances. This hypothesis now is generally accepted. The effect of imperfections is most severe for axially compressed, unstiffened cylinders. Similar discrepancies, though generally not as severe, have been observed for other loading conditions and shell shapes. In addition to geometric imperfections, experimental and theoretical evidence also has shown that the buckling load may be affected by the boundary conditions and by residual stresses introduced during the manufacturing process. Residual stresses change the effective process. Residual stresses change the effective stress-strain curve of the material and cause inelastic action to begin before the yield point is reached. As a result, the buckling process is hastened. The elastic postbuckling behavior of perfect and imperfect, axially compressed, unstiffened thin cylinders is demonstrated qualitatively in Fig. 1. There is a sudden decrease in load carrying capacity upon buckling. Because there is no postbuckling reserve strength, the buckling of an axially compressed, unstiffened cylinder is coincident with failure. Moreover, the failure is sudden and drastic. For this reason, the relative confidence level in the buckling load should be higher for unstiffened cylinders than for most other structural elements. This is made difficult by the lack of agreement between theoretical and experimental results for unstiffened cylinders. Therefore, these cylinders should be designed conservatively. To improve their resistance to buckling, large-diameter cylinders frequently are stiffened using longitudinal stiffeners (called stringers) and circumferential stiffeners (called rings). Stiffened cylinders behave better than their unstiffened counterparts, as demonstrated qualitatively in Fig. 2. Two aspects of the behavior of stiffened cylinders are significant. First, the detrimental effect of geometric imperfections is less pronounced than that for unstiffened cylinders. Second, the decrease in load capacity on buckling is much smaller than that for unstiffened cylinders. Thus, stiffened cylinders are not characterized by sudden drastic failures compared with unstiffened cylinders. JPT P. 668

Prediction of transverse strength and scatter in test data for unidirectional composites : Greszczuk, L. B. Conference on Composite Reliability, ASTM STP 580 (American Society for Testing and Materials, 1975) pp 311–326

Prediction of transverse strength and scatter in test data for unidirectional composites : Greszczuk, L. B. Conference on Composite Reliability, ASTM STP 580 (American Society for Testing and Materials, 1975) pp 311–326