Resilient Energy

1943 ◽  
Vol 16 (3) ◽  
pp. 591-608
Author(s):  
E. C. B. Bott
Keyword(s):  
Tensile Strength ◽  
Finite Differences ◽  
Practical Method ◽  
Cross Sectional Area ◽  
Point Of View ◽  
Sectional Area ◽  
Cross Sectional ◽  
Vulcanized Rubber ◽  
Reinforcing Agent ◽  
Strength Based

Abstract 1. The tensile strength of vulcanized rubber may be expressed in terms of its elongation by means of the calculus of finite differences. 2. This expression for tensile strength, based on the theoretical cross-sectional area, gives an expression for the tensile strength based on the original cross-sectional area when the former quantity is divided by the factor (E + 1), E being the elongation. 3. The expression for tensile strength based on the original cross-sectional area is integrated with respect to the elongation to give the resilient energy. 4. The trapezoidal rule has proved itself to be superior to the calculus of finite differences as a practical method of obtaining the resilient energy. 5. The total resilient energies are plotted on graphs against the percentage by volume of reinforcing agent or filler. Tangents drawn at any desired point corresponding to a certain percentage of filler give values for the partial resilient energies of base mix and of filler by the method of tangent intercepts. 6. The expressions for tensile strength are composed of one, two or three functions ; the number of functions is, in general, inversely proportional to the percentage of the filler in the vulcanizate. 7. The expressions for tensile strength and for resilient energies have no significance regarding the structure of vulcanized rubber; they have been evolved from the point of view of usefulness for evaluating compounds. 8. The values of the partial resilient energies of base mix and of filler obtained by the method of tangent intercepts have no physical meaning; they are a means of calculating the total resilient energy of a sample of vulcanized rubber.

Effect of Weld Defects on Tensile Properties of Lightweight Materials and Correlations With Phased Array Ultrasonic Nondestructive Evaluation

2014 ◽  
Author(s):  
Mohammad W. Dewan ◽  
M. A. Wahab ◽  
Ayman M. Okeil
Keyword(s):  
Tensile Strength ◽  
Aluminum Alloy ◽  
Tensile Properties ◽  
Phased Array ◽  
Critical Value ◽  
Area Ratio ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Strength And Toughness

Fusion welding of Aluminum and its alloys is a great challenge for the structural integrity of lightweight material structures. One of the major shortcomings of Aluminum alloy welding is the inherent existence of defects in the welded area. In the current study, tests have been conducted on tungsten inert gas (TIG) welded AA6061-T651 aluminum alloy to determine the effects of defect sizes and its distribution on fracture strength. The information will be used to establish weld acceptance/rejection criteria. After welding, all specimens were non-destructively inspected with phased array ultrasonic and measured the projected area of the defects. Tensile testing was performed on inspected specimens containing different weld defects: such as, porosity, lack of fusion, and incomplete penetration. Tensile tested samples were cut along the cross section and inspected with Optical Microscope (OM) to measure actual defect sizes. Tensile properties were correlated with phased array ultrasonic testing (PAUT) results and through microscopic evaluations. Generally, good agreement was found between PAUT and microscopic defect sizing. The tensile strength and toughness decreased with the increase of defect sizes. Small voids (area ratio <0.04) does not have significant effect on the reduction of tensile strength and toughness values. Once defective “area ratio (cross sectional area of the defect) / (total specimen cross sectional area)” reached a certain critical value (say, 0.05), both strength and toughness values decline sharply. After that critical value both the tensile strength and toughness values decreases linearly with the increase of defect area ratio.

scholarly journals RELATIONSHIP BETWEEN ISOMETRIC CERVICAL EXTENSION STRENGTH BASED ON A CERVICAL EXTENSION MACHINE AND THE CROSS-SECTIONAL AREA OF NECK MUSCLES

2000 ◽  
Vol 49 (1) ◽  
pp. 193-201 ◽  
Author(s):  
KAORU TSUYAMA ◽  
YOUSUKE YAMAMOTO ◽  
HIDEO FUJIMOTO ◽  
KOUICHI NAKAZATO ◽  
HITONE FUJISHIRO ◽  
...  
Keyword(s):  
Neck Muscles ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Strength Based ◽  
The Cross

scholarly journals Bimodal optimization with constraints: Critical value of the constraint and post-critical configurations

2011 ◽  
Vol 38 (2) ◽  
pp. 107-124
Author(s):  
Teodor Atanackovic ◽  
Alexander Seyraniany
Keyword(s):  
Total Energy ◽  
Critical Value ◽  
Optimal Shape ◽  
Cross Sectional Area ◽  
Point Of View ◽  
Sectional Area ◽  
Cross Sectional ◽  
Critical Configurations ◽  
Bimodal Optimization ◽  
Elastic Column

By using a method based on Pontryagin?s principle, formulated in [13], and [14] we study optimal shape of an elastic column with constraints on the minimal value of the cross-sectional area. We determine the critical value of the minimal cross-sectional area separating bi from unimodal optimization. Also we study the post-critical shape of optimally shaped rod and find the preferred configuration of the bifurcating solutions from the point of view of minimal total energy.

Tensile strength of partially filled FFF printed parts: meta modelling

2017 ◽  
Vol 23 (3) ◽  
pp. 524-533 ◽  
Author(s):  
Shahrain Mahmood ◽  
A.J. Qureshi ◽  
Kheng Lim Goh ◽  
Didier Talamona
Keyword(s):  
Mathematical Model ◽  
Tensile Strength ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Fused Filament Fabrication ◽  
Cross Sectional ◽  
Content Type ◽  
Test Pieces ◽  
Solid Part ◽  
The Cross

Purpose This paper aims to investigate the tensile strength of partially filled fused filament fabrication (FFF) printed parts with respect of cross-sectional geometry of partially filled test pieces. It was reported in the authors’ earlier work that the ultimate tensile strength (UTS) is inversely proportional to the cross-sectional area of a specimen, whereas the number of shells and infill density are directly proportional to the UTS with all other parameters being held constant. Here, the authors present an in-depth evaluation of the phenomenon and a parametric model that can provide useful estimates of the UTS of the printed part by accounting for the dimensions of the solid floor/roof layers, shells and infills. Design/methodology/approach It was found that partially filled FFF printed parts consist of hollow sections. Because of these voids, the conventional method of determining the UTS via the gross cross-sectional area given by A = b × h, where b and h are the width and thickness of the printed part, respectively, cannot be used. A mathematical model of a more accurate representation of the cross-sectional area of a partially filled part was formulated. Additionally, the model was extended to predict the dimensions as well as the lateral distortion of the respective features within a printed part using input values from the experimental data. Findings The result from this investigation shows that to calculate the UTS of a partially filled FFF part, the calculation based on the conventional approach is not sufficient. A new meta-model is proposed which takes into account the geometry of the internal features to give an estimate of the strength of a partially filled printed part that is closer to the value of the strength of the material that is used for fabricating the part. Originality/value This paper investigates the tensile strength of a partially filled FFF printed part. The results have shown that the tensile strength of a partially filled part can be similar to that of a solid part, at a lower cost: shorter printing time and lower material usage. By taking into account the geometries within a printed part, the cross-sectional area can be accurately represented. The mathematical model which was developed would aid end-users to predict the tensile strength for a given set of input values of the process parameters.

Effect of Intercritical Quenching on Microstructure and Mechanical Properties of Oil Casing Steel N80

2013 ◽  
Vol 395-396 ◽  
pp. 279-283
Author(s):  
Min Huang ◽  
Yu Wang ◽  
Ya Ni Zhang ◽  
Yue Wei Xie ◽  
Shuo Feng Li
Keyword(s):  
Tensile Strength ◽  
High Strength ◽  
Optical Microscope ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Scanning Calorimetry ◽  
Cross Sectional ◽  
Study Results ◽  
The Impact ◽  
The Sacrifice

In order to improve the toughness of oil casing steel N80 without the sacrifice of its original high strength, an intercritical quenching treatment was conducted under the temperature determined by a differential scanning calorimetry (DSC) analysis. Effects of intercritical quenching on the microstructure of oil casing steel N80 were characterized by means of optical microscope (OM) and scanning electron microscope (SEM). Tensile strength, reduction of cross-sectional area and microhardness were measured to evaluate the mechanical property of oil casing steel N80 after intercritical quenching treatment. The study results show that the tensile strength and microhardness of intercritical quenched oil casing steel N80 consisting of ferrite (F) and martensite (M) is slightly lower than that of tempered oil casing steel N80 composing of sorbite (S), yet which is still higher than that of full annealled oil casing steel N80 composing of pearlite (P) and a little amount of ferrite (F). In particular, the reduction of cross-sectional area of oil casing steel N80 intercritical quenched at 740°C is higher than those of tempered and full annealled. Additionally, both dimple and cleavage can be found on the impact fracture surface of N80 steel after intercritical quenching at 740°C. The toughness of oil casing steel N80 can be obviously improved by the intercritical quenching treatment at 740°C due to the formation of ferrite (F).

Tensile strength of partially filled FFF printed parts: experimental results

2017 ◽  
Vol 23 (1) ◽  
pp. 122-128 ◽  
Author(s):  
Shahrain Mahmood ◽  
A.J. Qureshi ◽  
Kheng Lim Goh ◽  
Didier Talamona
Keyword(s):  
Tensile Strength ◽  
Conventional Method ◽  
Process Parameters ◽  
Preliminary Investigation ◽  
Cross Sectional Area ◽  
Specimen Thickness ◽  
Sectional Area ◽  
Fused Filament Fabrication ◽  
Cross Sectional ◽  
Content Type

Purpose This paper aims to discuss the effect of changes of a comprehensive list of process parameters on part scalability and tensile strength of fused filament fabrication (FFF) printed parts. A number of parameters hitherto not studied such as cross-sectional area and its interaction with number of shells and infill density are presented and studied. Design/methodology/approach From a preliminary investigation, results have shown that varying the process parameters affects the ultimate tensile strength (UTS) of a FFF printed component, with component scale and number of shells as the two most significant parameters affecting the UTS. A further investigation based on the interactions of four process parameters, specimen width, b, specimen thickness, h, number of shells, n, and infill density, i, and their effects on the UTS was performed. Taguchi’s design of experiment was used to develop an experimental plan in this investigation. Specimens were printed and tested for their tensile strength until fracture and the results analyzed. Findings Results obtained support an inverse relationship between part scalability, change in cross-sectional area and the UTS of a FFF printed part. The UTS results were calculated in line with conventional method based on the gross cross-sectional area of A = (b × h). Originality/value The paper investigates the effect of part scalability on the UTS of FFF printed parts and evaluates the conventional method of calculating material tensile strength of FFF printed parts using the gross cross-sectional area of A = (b × h). The results of this findings show that the conventional method cannot be used as FFF printed parts consists of partially filled parts and not a solid component.

Mechanical properties of the collagenous framework of skin in rats of different ages

1964 ◽  
Vol 206 (6) ◽  
pp. 1425-1429 ◽  
Author(s):  
Phyllis Fry ◽  
Margaret L. R. Harkness ◽  
R. D. Harkness
Keyword(s):  
Mechanical Properties ◽  
Tensile Strength ◽  
Unit Area ◽  
Constant Load ◽  
Cross Sectional Area ◽  
Mechanical Resistance ◽  
Sectional Area ◽  
Cross Sectional ◽  
Constant Rate ◽  
Zero Time

The collagen content, tensile strength, and extensibility of the skin of rats have been examined in rats 3–85 weeks of age. Tensile strength calculated per unit cross-sectional area of collagen increased with age, the maximal value in the oldest group (5.5 kg/mm2 collagen) being about three times that in the youngest. The quantity present per unit area of surface also increased with age. An estimate of the total "surface mechanical resistance" obtained by multiplying collagen per unit area of skin and tensile strength rose continuously about twentyfold between the youngest to oldest of the groups. Application of a load produces after a time an elongation at constant rate ( K). Extensibility, measured by the ratio of this rate to length at zero time ( l0) obtained by extrapolation, and corrected to constant load of 100 g/mm2 cross-sectional area of collagen, was found to fall with age, the range being about eightyfold.

scholarly journals A New Approach on Vibrating Horns Design

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Maria Violeta Guiman ◽  
Ioan Călin Roșca
Keyword(s):  
Optimization Design ◽  
Nodal Point ◽  
Optimization Method ◽  
Cross Sectional Area ◽  
Point Of View ◽  
Sectional Area ◽  
Cross Sectional ◽  
New Approach ◽  
Frequency Maximum ◽  
Predicted Values

An optimization method of the vibrating horns is presented considering the smallest action principle and the attached cutting tool mass. The model is based on Webster’s wave propagation equation and as an objective function the minimization of the volume in structural equilibrium conditions was considered. The considered input parameters were working frequency, maximum cross-sectional area, magnification coefficient, and the attached mass. At the end of the study, a new shape function of the horn’s cross section is obtained. The particularity of the new obtained shape is given by the nodal point position that is the same with the position of the maximum cross-sectional area. The obtained horn was analyzed from the modal point of view using theoretical and experimental methods. As theoretical methods, both the state-space method and the finite element method were used. An experimental setup for frequency response function determination was developed using a random input signal. The verification of the magnitude value was done considering a harmonic steady-state signal. The recorded values were compared with the predicted values. The numerical simulations and tests support the validity of the assumptions used in the horns optimization design.

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