An Experimental Investigation of Elastic-Plastic Pulse Propagation in Aluminum Rods

1967 ◽  
Vol 34 (1) ◽  
pp. 91-99 ◽  
Author(s):  
S. R. Bodner ◽  
R. J. Clifton
Keyword(s):  
Room Temperature ◽  
Elevated Temperatures ◽  
Strain Curve ◽  
Static Stress ◽  
Stress Strain Curve ◽  
Proportional Limit ◽  
Stress Strain ◽  
Elastic Plastic ◽  
Time Profiles ◽  
The Impact

Experiments are reported involving elastic-plastic pulses due to explosive loading at one end of long, annealed, commercially pure, aluminum rods at room temperature and at elevated temperatures up to 750 deg F. The stress waves were detected by a condenser microphone at the far end of the rod and, in some cases, by strain gages at a cross section distant from the impact end. The essential features of the recorded velocity-time profiles and strain-time profiles are found to be in agreement with the predictions of rate independent elastic-plastic theory which takes a Bauschinger effect into account. At room temperature, the reference dynamic stress-strain curve does not differ appreciably from the quasi-static stress-strain curve whereas at elevated temperatures there appears to be a marked difference between the dynamic and quasi-static stress-strain curves. The experiments also serve to determine the dynamic proportional limit which is found to be fairly insensitive to temperature. Since the maximum plastic strains are small at cross sections remote from the impact end, the measurements, and consequently the conclusions, are limited to small strains beyond the proportional limit.

Stress-strain curve of paper revisited

2012 ◽  
Vol 27 (2) ◽  
pp. 318-328 ◽  
Author(s):  
Svetlana Borodulina ◽  
Artem Kulachenko ◽  
Mikael Nygårds ◽  
Sylvain Galland
Keyword(s):  
Three Dimensional ◽  
Strain Curve ◽  
Failure Behavior ◽  
Three Dimensional Model ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Fiber Network ◽  
Bonding Parameters ◽  
Particle Level ◽  
The Impact

Abstract We have investigated a relation between micromechanical processes and the stress-strain curve of a dry fiber network during tensile loading. By using a detailed particle-level simulation tool we investigate, among other things, the impact of “non-traditional” bonding parameters, such as compliance of bonding regions, work of separation and the actual number of effective bonds. This is probably the first three-dimensional model which is capable of simulating the fracture process of paper accounting for nonlinearities at the fiber level and bond failures. The failure behavior of the network considered in the study could be changed significantly by relatively small changes in bond strength, as compared to the scatter in bonding data found in the literature. We have identified that compliance of the bonding regions has a significant impact on network strength. By comparing networks with weak and strong bonds, we concluded that large local strains are the precursors of bond failures and not the other way around.

Definition of the yield point in plasticity and its effect on the shape of the yield locus

1966 ◽  
Vol 1 (4) ◽  
pp. 331-338 ◽  
Author(s):  
T C Hsu
Keyword(s):  
Yield Point ◽  
Experimental Work ◽  
Strain Curve ◽  
Yield Locus ◽  
Experimental Results ◽  
Stress Strain Curve ◽  
Proportional Limit ◽  
Stress Strain ◽  
Small Section ◽  
Definition Of

Three different definitions of the yield point have been used in experimental work on the yield locus: proportional limit, proof strain and the ‘yield point’ by backward extrapolation. The theoretical implications of the ‘yield point’ by backward extrapolation are examined in an analysis of the loading and re-loading stress paths. It is shown, in connection with experimental results by Miastkowski and Szczepinski, that the proportional limit found by inspection is in fact a point located by backward extrapolation based on a small section of the stress-strain curve, near the elastic portion of the curve. The effect of different definitions of the yield point on the shape of the yield locus and some considerations for the choice between them are discussed.

Dynamic Stress-Strain Relations for Annealed 2S Aluminum Under Compression Impact

1953 ◽  
Vol 20 (4) ◽  
pp. 523-529
Author(s):  
J. E. Johnson ◽  
D. S. Wood ◽  
D. S. Clark
Keyword(s):  
Dynamic Stress ◽  
Strain Curve ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Impact Stress ◽  
Stress Strain Relation ◽  
Final Strain ◽  
Dynamic Relations ◽  
Single Stress ◽  
The Impact

Abstract This paper presents the results of an experimental study of the stress-strain relation of annealed 2S aluminum when subjected to compression impact. Two methods of securing a dynamic stress-strain curve are considered, namely, from the measurement of impact stress as a function of maximum plastic strain, and impact stress as a function of the impact velocity. The dynamic stress-strain curves obtained by these methods lie considerably above the static curve. The elevation in stress of the dynamic relations above the static relation increases progressively from zero at the elastic limit to about 20 per cent at a strain of 4.5 per cent. However, the two dynamic relations are not coincident which indicates that the behavior of the material cannot be described by a single stress-strain curve for all impact velocities. A family of stress-strain curves which differ slightly from each other and which depend upon the final strain is postulated in order to correlate both sets of data adequately.

The Behavior of Raw Rubber When Stretched Isothermally

1938 ◽  
Vol 11 (4) ◽  
pp. 647-652 ◽  
Author(s):  
H. Hintenberger ◽  
W. Neumann
Keyword(s):  
Room Temperature ◽  
Strain Curve ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Steep Ascent ◽  
Flow Effect ◽  
Vulcanized Rubber ◽  
Flow Phenomena ◽  
Entropy Effect ◽  
The Subject

Abstract The S-shaped form of the stress-strain curve of rubber is today explained in a quite satisfactory way. In the first part of the curve, i. e., the gradual ascent, work must be expended because of the van der Waals forces of attraction of the molecules; in the second part, i. e., the steep ascent, the elasticity is chiefly an entropy effect, which is finally exceeded by crystallization phenomena. The phenomenon of crystallization itself has been the subject of extensive investigations, but in most cases vulcanized rubber has been employed, and because of the various accelerators and fillers which the rubber has contained, the products have been rather ill-defined. It is evident that the phenomena involved in crystallization would be much more clearly defined if the substance under investigation were to be in a higher state of purity. If experiments are carried out with raw rubber, a flow effect is added to the various other phenomena. As a result of this flow effect, Rosbaud and Schmidt, and Hauser and Rosbaud as well, found that the stress-strain curve depends on the rate of elongation at very low extensions, with a greater stiffness at high rates of elongation. As found recently by Kirsch, there is no evidence of any flow phenomena in vulcanized rubber at room temperature. Most investigations have been so carried out that the stress has been measured at a definite elongation. It was therefore of interest to determine the elongation at constant stress, and the changes in this relation with time and with temperature, of various types of raw rubber.

Deformational characteristics of thermally treated sandstone from an underground coalmine fire region, India

2021 ◽  
Author(s):  
Adarsh Tripathi ◽  
Noopur Gupta ◽  
Ashok Kumar Singh ◽  
Nachiketa Rai ◽  
Anindya Pain
Keyword(s):  
Large Scale ◽  
Elevated Temperatures ◽  
Strain Curve ◽  
Small Scale ◽  
Carbonaceous Shale ◽  
Deformation Pattern ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Thermomechanical Behaviour ◽  
Thermally Treated

<p>The Jharia region of lower Gondwana in India is one of the largest Underground Coalmine Fires (UCF) affected coalfield in the world. The UCF induced small scale as well as large-scale surface fracturing often creates the life-threatening conditions to coal miners and local surroundings. So, there is a need to understand the thermomechanical behaviour of coal measures rocks to predict the land disturbances in thermo-environmental conditions. It will provide an insight into the UCF induced subsidence mechanism and its preventive measures. The Jharia coal field predominantly consists of sandstone (75-80% by volume) and rest is composed of coal, shale and carbonaceous shale. The present study focuses on thermo-mechanical behaviour of Barakar sandstone (BS) under elevated temperatures. The cores of BS sample were prepared according to the ISRM standards. Further, samples were grouped and thermally treated in temperature range of 25°C, 100°C, 150°C, 300°C, 400°C, 500°C, 600 °C, 700°C and 800°C at a heating rate of 5°C/min for 24 hours in furnace.  Then, these thermally treated BS samples were subjected to laboratory test for stress-strain characteristics. In the process of deformational characteristics evaluation, effect of mineralogical changes and mode of fracture pattern were also studied at the mentioned elevated temperature. Based on the obtained results, the deformational behaviour of thermally treated BS specimens can be grouped into three zones, viz., zone 1 (25-300°C), zone 2 (300-500°C) and zone 3 (500-800°C). In zone 1, the characteristics of the stress-strain curve is similar to those under air dried sandstone specimen. However, small increment in stiffness were observed upto 300°C. The stress-strain curves in this zone shows dominantly brittle fracturing. The increment in stiffness may be related to evaporation of pore water that increases the cohesion between the mineral grains resulting higher stiffness value. In zone 2, the deformation pattern again shows brittle fracturing with continuous decrement in stiffness. The reduction in stiffness may be related to thermally induced porosity and increased microcrack density. In zone 3, the stress strain curve is observed to be concave upward. It indicates the pseudo-ductile behaviour of the thermally treated BS specimens. The observed results suggest a typical behaviour of deformation pattern under UCF induced rock fracturing which may be useful in predicting the land subsidence in UCF affected areas. Present research outcome may be used to design the support measures to reduce the associated hazards.</p>

Experimental Setup for the Determination of Mechanical Solder Materials Properties at Elevated Temperatures

2010 ◽  
Vol 638-642 ◽  
pp. 3793-3798
Author(s):  
Wolfgang H. Müller ◽  
Holger Worrack ◽  
Jens Sterthaus
Keyword(s):  
Mechanical Properties ◽  
Young’S Modulus ◽  
Elevated Temperatures ◽  
Young's Modulus ◽  
Linear Optimization ◽  
Strain Curve ◽  
Stress And Strain ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Non Linear

The fabrication of microelectronic and micromechanical devices leads to the use of only very small amounts of matter, which can behave quite differently than the corresponding bulk. Clearly, the materials will age and it is important to gather information on the (changing) material characteristics. In particular, Young’s modulus, yield stress, and hardness are of great interest. Moreover, a complete stress-strain curve is desirable for a detailed material characterization and simulation of a component, e.g., by Finite Elements (FE). However, since the amount of matter is so small and it is the intention to describe its behavior as realistic as possible, miniature tests are used for measuring the mechanical properties. In this paper two miniature tests are presented for this purpose, a mini-uniaxial-tension-test and a nanoindenter experiment. In the tensile test the axial load is prescribed and the corresponding extension of the specimen length is recorded, both of which determines the stress-strain- curve directly. The stress-strain curves are analyzed by assuming a non-linear relationship between stress and strain of the Ramberg-Osgood type and by fitting the corresponding parameters to the experimental data (obtained for various microelectronic solders) by means of a non-linear optimization routine. For a detailed analysis of very local mechanical properties nanoindentation is used, resulting primarily in load vs. indentation-depth data. According to the procedure of Oliver and Pharr this data can be used to obtain hardness and Young’s modulus but not a complete stress-strain curve, at least not directly. In order to obtain such a stress-strain-curve, the nanoindentation experiment is combined with FE and the coefficients involved in the corresponding constitutive equations for stress and strain are obtained by means of the inverse method. The stress-strain curves from nanoindentation and tensile tests are compared for two mate-rials (aluminum and steel). Differences are explained in terms of the locality of the measurement. Finally, material properties at elevated temperature are of particular interest in order to characterize the materials even more completely. We describe the setup for hot stage nanoindentation tests in context with first results for selected materials.

scholarly journals A study of the Cu0.95Al0.05 alloy: stress-strain curve and microstructure

2018 ◽  
Vol 20 (2) ◽  
Author(s):  
Emilio Medrano ◽  
Mauro Quiroga ◽  
Felipe A. Reyes
Keyword(s):  
Room Temperature ◽  
Single Phase ◽  
Strain Curve ◽  
Tensile Tests ◽  
Optical Microscope ◽  
Metal Alloys ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Electrolytic Copper ◽  
Mechanical Traction

After fabricating five metallographic specimens of the Cu0.95Al0.05 alloy from electrolytic copper and aluminum, these ones were both microstructurally characterized by using a metallographic optical microscope at room temperature and subjected to mechanical traction in order to chart the stress-strain curve. From the characterization, it has been found out that the Cu0.95Al0.05 microstructure is composed of a single phase, and from the tensile tests, it has been obtained its rupture point, 249.361 MPa. The obtained results were explained in the framework of the theory of metals and metal alloys.

Non-linear delamination fracture analysis by using power-law hardening

2016 ◽  
Vol 12 (1) ◽  
pp. 80-92 ◽  
Author(s):  
Victor Iliev Rizov
Keyword(s):  
Power Law ◽  
Strain Curve ◽  
Fracture Analysis ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Content Type ◽  
Elastic Plastic ◽  
Linear Fracture ◽  
Delamination Fracture ◽  
Non Linear

Purpose – The purpose of this paper is to perform a theoretical analysis of non-linear delamination fracture in cantilever beam opened notch (CBON) configuration. It is assumed that the non-linear mechanical behavior of the CBON can be described by using a stress-strain curve with power-law hardening. Design/methodology/approach – The fracture analysis is carried-out by applying the integration contour independent J-integral. For this purpose, a model based on the technical beam theory is used. Equation is derived for determination of the CBON specimen curvature in elastic-plastic stage of deformation. The equation is solved by using the MatLab program system. Solutions of the J-integral are obtained at linear-elastic as well as elastic-plastic behavior of the CBON. The influence of the power-law exponent on the non-linear fracture is evaluated. Findings – The analysis reveals that the J-integral value increases when the exponent of the power-law increases. The solution obtained here is very useful for parametric analyses of the non-linear fracture behavior, since the simple formulas derived capture the essentials of the fracture response. Practical implications – Beside for parametric investigations, the solution obtained here can also be applied for calculating the critical J-integral value at non-linear behavior using experimentally determined critical fracture load at the onset of crack growth from the initial crack tip position in the CBON configuration. Originality/value – An analysis is performed of the non-linear fracture in the CBON configuration by applying the J-integral approach, assuming that the mechanical response can be modeled using a stress-strain curve with power-law hardening.

Delamination analysis of a layered elastic-plastic beam

2017 ◽  
Vol 8 (5) ◽  
pp. 516-529 ◽  
Author(s):  
Victor Rizov
Keyword(s):  
Fracture Behaviour ◽  
Strain Curve ◽  
Integral Approach ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Content Type ◽  
Elastic Plastic ◽  
Lap Shear ◽  
Delamination Fracture ◽  
Non Linear

Purpose The purpose of this paper is to perform a theoretical analysis of delamination fracture behaviour of the Crack Lap Shear layered beam configuration taking into account the material non-linearity. A delamination crack located arbitrarily along the beam height was considered in this study. Design/methodology/approach The beam mechanical behaviour was described by using the Ramberg-Osgood stress-strain relation. Fracture was analysed by applying the J-integral approach. Besides by using symmetric Ramberg-Osgood stress-strain curve, fracture was investigated also by Ramberg-Osgood stress-strain curve that is not symmetric with respect to tension and compression. The J-integral solutions were verified by performing elastic-plastic analyses of the strain energy release rate. Findings The effects of crack location and material properties on the non-linear fracture behaviour were evaluated. It was found that the material non-linearity leads to increase of the J-integral values. Therefore, the material non-linearity has to be taken into account in fracture mechanics based safety design of structural members composed by layered materials. The analytical solutions derived are very useful for parametric investigations of delamination fracture with considering the material non-linearity. The results obtained can be applied for optimisation of the beam structure with respect to fracture performance. Originality/value The present study contributes for the understanding of delamination fracture in layered beams that exhibit non-linear material behaviour.

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