Four-point Bending Fixture Research Articles

Investigations on fatigue properties of red sandstone under positive and negative pure bending loads

Brittle materials such as rock and concrete may be subjected to positive and negative cyclic loading effects such as earthquakes and construction disturbances, and bending damage is one of the most likely forms of damage. A four-point bending fixture was designed to conduct fatigue tests with positive and negative stress ratios under pure bending to investigate the influence of cyclic loading on the form and mechanism of damage. The fracture energy calculation equation based on crack mouth opening displacement (CMOD) was derived, and the fracture criterion based on fracture toughness and fracture energy was established, which was in good agreement with the experimental results. Under the pure bending fatigue load, the hysteresis loop of the P-CMOD curve shows a loose-dense-loose law, and the damage curve can be divided into three stages of initial, stable, and accelerated law. Stress level and stress ratio are two main factors affecting fatigue life. The fatigue life of negative stress ratios is greater than that of positive stress ratios because there is a crack closure process in negative stress ratios, which affects the fatigue life. The final damage occurs for positive stress ratio specimens when the fatigue dissipation energy is greater than the static fracture energy. Static CMOD starting and final values were introduced to define the fatigue damage variables, and a damage evolution model was established better to simulate the evolution with positive and negative stress ratios.

Silicon MEMS Nanomechanical Membrane Flexure Sensor With Integrated High Gauge Factor ITO

Introduction of structural modification and novel transduction materials to nanomechanical cantilever (NMC) sensor can bring considerable improvement in sensor performance leading to ultra-sensitive nanomechanical sensor platforms. This work reports development of an optimized and highly sensitive silicon MEMS Nanomechanical Membrane-Flexure (NMF) piezoresistive surface stress sensor. This MEMS structure consists of a circular adsorbate membrane suspended by four inverse trapezoidal flexures. The electromechanical transduction of the sensor is performed by integrating a high gauge factor low temperature sputter deposited Indium Tin Oxide (ITO) thin film as piezoresistor. The ITO thin film was experimentally characterized for extracting its electrical, mechanical, and electromechanical properties to assess its candidature in integrating as strain sensing element with nanomechanical sensors. The gauge factor of ITO thin film was measured using a high precision four-point bending fixture experimental setup. An ultra-thin ITO film deposited at room temperature with no oxygen flow and post annealing treatments exhibited a high negative gauge factor of −430, making it an excellent candidate in nanomechanical sensor platform. The incorporation of sputter deposited ITO thin film as piezoresistive layer obviated the need for doping in silicon which further reduced the fabrication process complexity for NMF sensor. The NMF sensor fabrication following SOI based silicon MEMS process along with device characterization have also been carried out as part of this work. The optimized design of piezoresistive NMF sensor exhibited an improved surface stress sensitivity of nearly 15 times higher than conventional cantilever sensor and thereby opening new possibilities in bio-chemical and environmental sensing applications. [2021-0127]

Development of Doped Silicon Multi-Element Stress Sensor Rosette With Temperature Compensation

In this paper, a developed n-type piezoresistive three dimensional (3D) stress sensor with full temperature compensation is presented. The proposed sensing rosette benefits from the stress insensitivity of the full-circular n-type piezoresistor, oriented over (111) silicon plane, to detect only temperature changes for compensation. Moreover, the unique behavior of shear piezoresistive coefficient (π44) of n-Si is utilized to construct a piezorestive stress sensing rosette over (111) silicon plane that is capable of extracting 3D stress components. A prototype stress sensing chip was microfabricatedto test the capabilityof the developedsensing rosette to accurately extract stress applied on structures at different thermal environments. The fabricated sensing chip was subjected to different mechanical loads using a loading rig with four-point bending fixture. The testing was carried out over a temperature range of 0-50 °C. The results showed that the proposed sensing chip has the capability of capturing the stress applied at different temperatures. Also, the developed sensing rosette showed less sensitivity to the uncertainty in piezoresistive coefficients' values compared to the other developed 3D piezoresistive stress sensors.

Using a Hierarchical Weibull model to Predict Failure Strength of Different Glass Edge Profiles

The edge strength of glass is analyzed using a Weibull statistical framework based on 78 data samples from a range of experiments recorded in literature. Based on the analysis, a 45 MPa strength value (computed as the lower bound in a one-sided confidence interval at the 75% level for the 5-percentile in the distribution) could be conservatively used with arrised, ground and polished edges when related to a reference length of 100 mm at an applied stress rate of 2 MPa/s. The size effect can be represented by the usual weakest-link scaling formula with the Weibull modulus taken to be 8.0, 12.0, 8.0 and 6.5, respectively, for as-cut, arrised, ground and polished edges. It is estimated that static fatigue is best accounted for with a value of stress corrosion parameter about n = 16. The results are obtained with random sampling MC in a hierarchical modelling approach with the Weibull parameters treated as nested random variables. By accounting for the influence of glass supplier as a mixed-effect in a linear statistical model, it is found that supplier effects are significant and important to consider along with others due to, e.g., stress rate and edge length exposed to maximum stress. The data samples which are limited to glass tested in an ambient environment using four-point bending fixture, show that Weibull statistics generally scatter considerably. Numerical investigations with random sampling show that shape parameter estimates scatter substantially when sample size is limited, which can explain some of the observed variability in shape more so for ground and polished edges than for as-cut and arrised. For the as-cut edge, it is suggested that the shape parameter is scale-dependent. The Weibull parameters are also estimated using a clustered likelihood estimator under the condition that the shape factor has constant value for each edge type.

A New Temperature Transducer for Local Temperature Compensation for Piezoresistive 3-D Stress Sensors

In this paper, a new temperature transducer using full-circular n-type piezoresistor over (111) silicon plane is proposed as an accurate solution for local temperature compensation for piezoresistive three-dimensional (3-D) stress sensors. Analytical study, in this paper, showed that the proposed n-type full-circular piezoresisor over (111) has near-zero response under 3-D state of stress. As an experimental verification, a test device with n-type piezoresistive stress sensing elements oriented over (111) plane at 0° and 90° to crystallographic direction $[ {\bar{1}10} ]$ was microfabricated to test the capability of the proposed temperature compensator. The test device was subjected to a uniaxial load up to 50 MPa using a loading rig with four-point bending fixture. The testing was performed over a temperature range of 0–50 °С. The results showed that the proposed temperature transducer has a linear response to temperature excitation. The fabricated transducer is capable of accurately capturing the local temperature changes with maximum absolute error of ±0.8 °С. This compensation system is advantageous for piezoresistive stress/strain sensors, since the temperature transducer has the same thermal environment with the stress/strain-sensing rosette. Moreover, this technique does not require additional circuitry on the sensing device itself.

Strain induced exchange-spring magnetic behavior in amorphous (TbDy)Fe2 thin films

In this paper, we report a strain induced exchange-spring magnetic behavior in sputter deposited (TbDy)Fe2 amorphous thin films with phase-separated layers of (TbDy)-rich and Fe-rich at room temperature. The magnetic hysteresis loops at different strain levels were obtained with a magneto-optic Kerr effect set-up incorporating a mechanical four-point bending fixture. The unstrained film exhibits a typical ferrimagnetic hysteresis loop while the strained structure exhibits step-like hysteresis loops representative of an exchange-spring magnetic system. The mechanically strained film changes the coercivity/remanence values from positive to negative. The observed magnetic changes under strain are attributed to magnetic anisotropy modifications in the highly magnetoelastic TbDy-rich layer.

Modeling and experimental investigation of out-of-plane deformation on mechanical performance of composites manufactured by ATL

The change of mold normal curvature along the trajectory may result in out-of-plane waviness during the automated laying process, on which the layup speed and temperature would have an effect. A new parameter, deformation rate, was defined by combining the effect of mold curvature change rate and layup speed. A predicting model was proposed based on the fiber waviness and interlaminar sliding model to calculate the relationship between stiffness retention and the layup process parameters, including deformation rate and temperature. An experimental study on the effect of different deformation parameters on the tensile performance of composites was carried out based on a new manufacturing method of plated specimens with different levels of waviness by means of a four-point bending fixture. The experimental results showed that when the deformation temperature increases from 20℃ to 80℃, the tensile strength increases first and then decreases while the tensile module keeps increasing. While the deformation rate decreases from 0.40 to 0.04 mm−1/s, both tensile strength and module showed an increasing trend. The predicting model being validated by experimental results can be utilized to optimize the layup process parameter to satisfy the quality and efficiency requirements.

Compensation of Mechanical Stress-Induced Drift of Bandgap References With On-Chip Stress Sensor

Today’s smart sensor systems rely heavily on bandgap circuit techniques to achieve the required high accuracy. However, all presently known bandgap references show a notable lifetime drift of $\sim 1$ mV caused by instable mechanical stress in common plastic encapsulated packages. This paper proposes a versatile digital stress compensation scheme which works for arbitrary packages and silicon technologies. It uses a new mechanical stress sensor to measure the sum of in-plane normal stress components. The mechanical stress drifts of bandgap reference, stress, and temperature sensors were characterized on wafer stripes in a four-point bending fixture. With these results a compensation algorithm was derived. Mechanical stress drifts were provoked by thermal cycling measurements on samples in a quad flat no leads-like plastic encapsulated package after moisture soaking. These measurements show that the mechanical stress related drift of a Brokaw bandgap voltage can be reduced by about one order in magnitude over the whole automotive temperature range. Due to the low process spread of the proposed stress sensor only a single-trim at room temperature on wafer level is necessary.

Large Strain Four-Point Bending of Thin Unidirectional Composites

A large deformation four-point bending fixture was used to test thin unidirectional composite laminas primarily used in strain energy deployable space structures. The tests allowed investigation of the large strain elastic constitutive behavior of two aerospace-grade intermediate modulus carbon fibers, a high modulus carbon fiber, and a structural glass fiber. Thermoset plastic coupons reinforced with these fibers and ranging in thickness from 0.1 to 0.5 mm were tested. A nonlinear empirical constitutive model was used to represent fiber axial tensile and compressive behavior and through a structural model, predict coupon flexural response and estimate constitutive model parameters. Intermediate modulus carbon fibers were found to be significantly nonlinear with modulus linearly increasing with strain. At failure, the fiber tangent modulus in tension was 2 to 3.1 times higher than in compression. The modulus of glass fibers was essentially constant. High modulus carbon fibers exhibited a more complex response with flexural stiffness initially slightly increasing followed by a moderate reduction in stiffness and finally, a sharp reduction in stiffness and failure.

Influence of Drilling Parameters on the Accuracy of Hole-drilling Residual Stress Measurements

The objective of this research is to define drill speeds that produce acceptable results when using the hole-drilling technique for measuring residual stress. For this study, three common engineering materials; alloy 6061-T651 aluminum, 304 stainless steel, and A36 carbon steel were used. This was achieved by performing ESPI/hole-drilling stress measurement of a known applied stress in discrete rpm intervals ranging from 2-40K rpm for each material. To produce a known state of stress specimens were bent elastically in a four-point bend fixture. Stress measurements were taken using single-axis electronic speckle-pattern interferometry (ESPI). It was found that for 6061-T6 aluminum, accurate and repeatable results can be achieved between speeds of 2-40K rpm. For 304 stainless steel, result accuracy diminishes when drill speeds go below 6K rpm. The A36 steel had a large as-received stress gradient across the longitudinal dimension and was therefore removed from this study.

Compression After Impact and Fatigue of Reconsolidated Fiber-reinforced Thermoplastic Matrix Solid Composite Laminate

Carbon fiber-reinforced poly-phenylene sulfide laminate coupons were impacted at low-energy in a drop-tower machine and subsequently fatigued in a four-point bending fixture. The doubly damaged test pieces were then hot-press reconsolidated and inspected nondestructively by vibrothermography to check their structural integrity. The residual mechanical properties of the laminate in both the as-damaged and as-repaired conditions were determined by compression loading with the in-plane strain fields determined via a digital image correlation system. Cross-section views of damaged and repaired samples were analyzed by light optical microscopy and correlated to residual mechanical properties, as were the digital image correlation and nondestructive test results. Based on the values of stiffness and ultimate strength of the repaired laminates, 10J was inferred as the maximum impact energy at which it is worthwhile performing hot-press reconsolidation, in view of the applied fatigue history following impact.

Determination of Young's modulus and Poisson's ratio of thin films by X-ray methods

Accurate determination of Young's modulus and Poisson's ratio is critical when characterizing the mechanical properties of ultra-thin films. In this work, a method to simultaneously measure the Young's modulus and Poisson's ratio of thin films by X-ray techniques combined with a four-point bending fixture is presented. The four-point bending fixture was carried out to purposely induce stresses on the thin film and cause a curvature of the film/wafer system. The induced stresses were measured by the modified conventional X-ray diffraction for film measurements. At the same time, the curvature of the film/wafer system was measured by the X-ray rocking curve. With the film stress derived from the curvature according to the Stoney formula, both the Poisson's ratio and the Young's modulus were evaluated from the plot of lattice d-spacing changes (strain) versus cos2α sin2ψ. The method was applied to determine thin copper films (~180nm). The estimated Poisson's ratios ranged from 0.18 to 0.24. Compared to the 0.34 for bulk Cu, the deviation between the bulk and the film properties was above ~30%. The Young's modulus of the films is 116.7±2.9GPa, which was comparable to those reported in the literature for ~128GPa.

Characterization of Young’s modulus of silicon versus temperature using a “beam deflection” method with a four-point bending fixture

Abstract Young’s modulus ( E ) and Poisson’s ratio ( ν ) are dependent upon the direction on the silicon surface. In this work, E and ν of silicon have been calculated analytically for any crystallographic direction of silicon by using compliance coefficients ( s 11 , s 12 , and s 44 ), and the values of E are confirmed experimentally by using a “beam deflection” method with a four-point bending fixture. Experimental results for E as a function of temperature from −150 °C to +150 °C are presented for (0 0 1) and (1 1 1) silicon wafers.

A Structural Neural System for Real-time Health Monitoring of Composite Materials

A prototype structural neural system (SNS) is tested for the first time and damage detection results are presented in this study. The SNS is a passive online structural health monitoring (SHM) system that mimics the synaptic parallel computation networks present in the human biological neural system. Piezoelectric ceramic sensors and analog electronics are used to form neurons that measure strain waves generated by damage. The sensing of strain waves is similar to the proven nondestructive evaluation (NDE) technique of acoustic emission (AE) monitoring. Fatigue testing of a composite specimen on a four-point bending fiXture is performed, and the SNS is used to monitor the specimen for damage in real time. The prototype SNS used four sensors as inputs, but the number of inputs can be in the tens or hundreds depending on the type of SNS processor used. This is an area of continuing development. The SNS has two channels of signal output that are digitized and processed in a computer. The first output channel tracks the propagation of waves due to damage, and the second output channel provides the combined AE responses of the sensors. The data from these two channels are used to predict the location of damage and to qualitatively indicate the severity of the damage. Overall, this study shows that the SNS can detect damage growth in composites during operation of the structure, and the SNS architecture has the potential to tremendously simplify the AE technique for use in on-board SHM. Ten or more input neurons can be used, and still only two output channels are needed. Two levels of monitoring are possible using the SNS; a coarser SHM approach, or an on-board NDE approach. The SHM approach uses the SNS with a coarse grid of neurons to monitor and detect damage occurring in a general area during operation of the structure. The SNS will indicate where and when a more sensitive inspection is needed which can be done using ground-based NDE techniques. The on-board NDE approach uses the SNS with a fine coverage of neurons for highly sensitive NDE which continuously listens for damage and provides real-time processing and information about any damage in the structure and the performance limits and safety of the vehicle.

Oxidation-induced strengthening in ground silicon carbide

Silicon carbide has specific advantages over other structural ceramics, such as high temperature capability and excellent chemical stability. So silicon carbide is a promising candidate for high temperature structural materials as well as for corrosion resistance applications. Like brittle materials, however, strength of silicon carbide is closely related to the size and distribution of surface flaws such as machining-induced cracks, because of their inherent low toughness. Thus, a smooth polishing procedure after grinding is often needed in order to reduce the size of surface flaws, leading to an increase in cost of ceramic components. Moreover, the allowable flaws in ceramics are so small that it is almost impossible to detect the flaws and also difficult to remove them completely using machining techniques. As a result, the structural integrity of a ceramic component is seriously affected. A method, to heal a crack, could be considered to overcome this problem. Studies on crack healing have been reported for alumina [1–3], silicon nitride [4–6], silicon nitride/silicon carbide composite [7], Mullite/silicon carbide composite [8] and silicon carbide [9–12]. Our research group recently proposed a mechanism of crack healing and strengthening by pre-oxidation procedure in silicon carbide [11, 12]. The major observation is that the residual stress produced by the thermal expansion mismatch between silica (within cracks) and surrounding silicon carbide played a significant role in the strength increase. As the crack healing technique can be adopted in practical strength applications, considerable advantages can be expected either in the reliability or in the machining and inspection costs of ceramic components. In the above perspectives, the effect of pre-oxidation on strength of silicon carbide with grinding-induced surface cracks was investigated and reported in the present communication. SiC material (Hexoloy, Carborandom, Inc., USA) was received in a plate form. The microstructure of the material consisted of SiC grains smaller than 10 lm and average grain size is about 5 lm (see Fig. 1). The material was machined into flexure specimens of 3 mm · 4 mm · 40 mm. The specimen surface was ground using diamond wheels with girt sizes of 127 lm, 64 lm, 42 lm and 32 lm. Grinding conditions were: 3,300 rpm, 35 m/s peripheral wheel speed and 10 lm depth of cut. The specimens were mounted on a holder in such a manner that grinding was oriented along the width of the specimens (perpendicular to the tensile stresses applied during the strength measurement). The ground specimens were then heat-treated at 1,500 C for 50 h in air. The heating rate was 10 C/min and cooling was done by turning off the electric power of the furnace. For comparison, some heat treatment experiments were also conducted in vacuum under similar conditions. The microstructure was characterized by field-emission scanning electron microscopy (FESEM), Energy Dispersive X-ray (EDX) and X-ray Diffraction (XRD). The strength of specimens was measured using a four-point bending fixture with outer and inner spans of 30 mm and 10 mm, respectively at a crosshead speed of 0.5 mm/min, as per the standard procedure [13]. Specimens were placed in the fixture such that the surface containing grinding-induced cracks was in M. C. Chu (&) AE S. J. Cho AE G. J. Yoon AE H. M. Park Division of Chemical Metrology and Materials Evaluation, Korea Research Institute of Standard and Science, 1 Doryong-dong, Yuseong, Deajeon 305-600, Korea e-mail: chumin@kriss.re.kr

An Analysis Of Internal Strains In UnidirectionalAnd Chopped Graphite Fibre CompositesBased On X-ray Diffraction And Micro RamanSpectroscopy Measurements

In this paper, the method for the determination of internal strains in polymer matrix composites from the strain measurements in the embedded sensors has been examined. Two types of strain sensors embedded in either chopped graphite fibre/epoxy matrix composite or unidirectional graphite fibre/polyimide matrix composite were investigated. For the chopped fibre composite, we used Kevlar49 fibres (~10μm in diameter) as strain sensors, while aluminium inclusions with diameters ranging from 1 to 20μm were embedded in the unidirectional composite. Both composite plates with embedded sensors were subjected to external loads generated by a four-point bending fixture. Strains inside the sensors were measured using either x-ray diffraction (XRD) or micro Raman spectroscopy (MRS). A model based on the equivalent inclusion method (EIM) was used to extract the internal strains in composites from the measured strains inside the embedded sensors. It has been demonstrated that the geometrical features and the material properties of the embedded strain sensors may affect the accuracy of the extraction of the composite internal strains. The average interactions between the sensors were found to have only a minor effect on the strain determination in a composite.

Initiation of stress-corrosion cracking in unidirectional glass/polymer composite materials

The purpose of this research is to determine the resistance to stress-corrosion cracking (SCC) of three unidirectional (pultruded) E-glass/polymer composites based on modified polyester, epoxy and vinyl ester resins. The composites have been subjected to a nitric acid solution of pH 1.2 in a newly designed four-point bend fixture. The stress-corrosion process was initiated on the as-supplied surfaces of the composites. The process has been monitored for acoustic emissions and the stress-corrosion surface damage in the specimens was investigated by the use of scanning electron microscopy. Experimental results indicate that the stress-corrosion cracks originate predominantly from exposed glass fibers on the surfaces of the composites. The process can be successfully monitored by means of acoustic emission equipment. Three stages of SCC, crack initiation, sub-critical crack extension and stable crack propagation, can be distinguished by carefully examining the curves of acoustic emission (number of events) versus time. For the first and second stages of SCC, the acoustic emission outputs are linear functions of time. The slopes of the first and second stages of the curves of acoustic emission versus time have been used to determine quantitatively both the resistance of the composites to crack initiation and sub-critical crack extension, respectively. It has been shown in this research that the resistance to the initiation of SCC in nitric acid of the E-glass/vinyl ester composite is approximately 10 times greater than the E-glass/epoxy composite. Furthermore, the E-glass/epoxy system exhibits approximately 5 times higher resistance to the initiation of SCC than the E-glass/modified polyester system. The sub-critical crack extension process is also significantly more rapid in the E-glass/modified polyester than in the E-glass/epoxy composite.

Fracture of fused silica with 351 nm laser-generated surface cracks

Laser-induced-surface-flaw experiments on fused silica at 351 nm and 500 ps pulse duration are reported here. Specimens with surface flaws produced at a measured exit-surface damage threshold fluence of Fexit/th = 10 J/cm2 were irradiated at a constant fluence of FL = 1.8 × Fexit/th by different numbers of laser pulses, N = 110 to 520. Micrograph observations show that (i) the produced cracks have a semielliptical shape and (ii) the material strength predictions based on the radial crack depth (normal to the surface) instead of the crack surface length (parallel to the surface) are in good agreement with measured strengths obtained using a four-point bending fixture. The underlying basis of conventional crack analysis is first examined critically and is argued to be deficient in the way the failure strength for the cracks is related to the characteristic parameters of crack geometry. In general, it is necessary to incorporate a residual term into the failure strength formulation. The crack depth and the failure strength are found to increase and decrease with the number of laser pulses, respectively.

The effect of loading rate on chevron notch fracture toughness measurements

One common concern with the manual testing of chevron notched specimens to determine fracture toughness is that it does not provide for precise control over the loading rate. This study examines the effect of loading rate on the measured fracture toughness of 20 identical hardened AISI 4140 steel samples. Eight samples were tested in a servohydraulic testing machine using a four-point bend fixture and four different ram speeds to produce total testing times of 1.1, 4.4, 16.7 and 69 sec. In addition 12 samples were tested in the Toughness Tool, a device similar to a torque wrench, that measures the maximum moment required to fracture a chevron notched four-point bend sample. Samples were tested in this device using fast, natural and slow loading rates corresponding to testing times of 0.7, 3.5 and 23 sec, respectively. Both sets of tests reveal that loading rate has no effect on the measured fracture toughness. Moreover, it is shown that the loading rate introduced by the Toughness Tool is easily controlled to within ± 15%. Therefore, the loading rate variability introduced by the new device is much smaller than that provided for in ASTM E1304, the standard for chevron notch fracture toughness testing, in which the loading rate range is permitted to vary over a factor of four.

Creep of silicon nitride-titanium nitride composites

The effect of particulate TiN additions (0–50 wt%) on creep behaviour of hot-pressed (5 wt%Y2O3 + 2 wt%Al2O3)-doped silicon nitride (HPSN)-based ceramics was studied. Creep was measured using a four-point bending fixture in air at 1100–1340 °C. At 1100 °C, very low creep rates of HPSN with 0–30 wt% TiN are observed at nominal stresses up to 160 MPa. At 1200 °C the creep rate is slightly higher, and at 1300 °C the creep rate is increased by three orders of magnitude compared to 1100 °C and rupture occurs after a few hours under creep conditions. It was established that the formation of a TiN skeleton could detrimentally affect the creep behaviour of HPSN. An increase in TiN content leads to higher creep rates and to shorter rupture times of the samples. Activation energies of 500–1000 kJ mol−1 in the temperature range of 1100–1340 °C at 100 MPa, and stress exponentsn⩽4 in the stress range 100–160 MPa at 1130–1200 °C were calculated. Possible creep mechanisms and the effect of oxidation on creep are discussed.