An analytical approach for relating hardness and yield strength for materials with high ratio of yield strength to Young modulus

2004 ◽  
Vol 841 ◽  
Author(s):  
Luc J. Vandeperre ◽  
Finn Giuliani ◽  
William J. Clegg

ABSTRACTFor materials with a high ratio of Y to the elastic modulus, E, experimental data show that the ratio of the hardness to the flow stress decreases from 3 toward 1 as Y / E increases. This behaviour is predicted by finite element calculations but to date analytical expressions have not been able to correctly predict the relation between Y and H nor have they been able to show how the geometry of the indenter is important. Therefore, in this paper the correlation between H and Y for such materials is re-examined using an analytical approach to provide a physical interpretation, which explains the trends observed.

Author(s):  
C. Sklorz ◽  
F. Otremba ◽  
F. Reich

Limit load analysis is a well known method to calculate the allowable design pressure of container components. A limit load of a pressurized container is achieved, when the stress of a wall and the flow stress are equal. In the following paper the transferability of limit load analysis from small scale tank containers up to large scale containers (railway tank) are investigated. Finite element calculations are carried out and compared with experimental results. It can be concluded that the limit load analysis works very well. Furthermore, the yield strength of the material should be used as flow stress.


1983 ◽  
Vol 50 (4a) ◽  
pp. 896-897 ◽  
Author(s):  
G. H. Kaufmann ◽  
A. M. Lopergolo ◽  
S. Idelsohn

The usefulness of using the speckle photography technique in fracture mechanics to check numerical calculations is demonstrated for an internally pressurized cylinder with a surface flaw. A pointwise technique was utilized to measure the opening displacements along the crack line and the Mode I stress-intensity factor was determined by extrapolating these results to the crack tip. Finite element calculations were performed to be compared with experimental data and good agreement was obtained.


2013 ◽  
Vol 647 ◽  
pp. 683-687
Author(s):  
Mi Gong ◽  
Hong Chao Kou ◽  
Yu Song Yang ◽  
Guang Sheng Xu ◽  
Jin Shan Li ◽  
...  

The pore structures on mechanical properties of porous Ti were investigated by 3D finite element models. Calculated elastic modulus and yield strength suggested that square-pore models exhibit lower modulus and higher strength compared with another two kinds of shapes (circle and hexagonal). In addition, under the condition of medium porosity (58.96%), integrated property was found in square-pore model which elastic modulus was 26.97GPa, less than 1/3 of hexagonal-pore model; while the yield strength maintained 63.82MPa, doubled the figure of circle-pore model. Thus, models with square-pore structures show potential perspective as hard tissue replacements. Investigation on anisotropy of microstructure implies that the elastic modulus was affected more intensively than the yield strength.


Author(s):  
Ahmadreza Eshghinejad ◽  
Mohammad Elahinia

Bending is a common mode of application and operation of shape memory alloys (SMA). So far the coupled thermomechanical behavior of these alloys have been modeled with numerical methods such as finite element. The issue in developing exact solutions for a SMA beam in bending is because of the distributed and hysteric stress-strain profile. In this paper an analytical approach is developed to find the exact solution for the displacement due to the applied force on the SMA superelastic beam. The approach is based on the assumption of linear distribution of strain along the height of a cross section in the beam. The solution is validated by experimental data and the results of the solution for a superelastic beams for different cases are illustrated.


Author(s):  
D G Walsh ◽  
A A Torrance ◽  
J Tiberg

Although thermally induced tensile residual stresses have been known to occur in ground components, it has not been possible to predict the critical temperature at which these stresses begin to manifest themselves in the workpiece. In this paper, a model of the formation of thermally induced tensile residual stresses is proposed and a simple method of calculating the critical temperature above which tensile residual stresses occur is developed. The analysis makes use of dimensional methods to characterize the critical temperature. In addition, a formula characterizing the yield strength as a function of temperature was developed. The model was then validated using finite element techniques and some experimental data. The analysis reveals that it is possible to determine the critical temperature above which tensile residual stresses will be manifested based on readily available material properties. A case study illustrates the application of the technique.


2014 ◽  
Vol 136 (9) ◽  
Author(s):  
Ameet K. Aiyangar ◽  
Juan Vivanco ◽  
Anthony G. Au ◽  
Paul A. Anderson ◽  
Everett L. Smith ◽  
...  

Most studies investigating human lumbar vertebral trabecular bone (HVTB) mechanical property–density relationships have presented results for the superior–inferior (SI), or “on-axis” direction. Equivalent, directly measured data from mechanical testing in the transverse (TR) direction are sparse and quantitative computed tomography (QCT) density-dependent variations in the anisotropy ratio of HVTB have not been adequately studied. The current study aimed to investigate the dependence of HVTB mechanical anisotropy ratio on QCT density by quantifying the empirical relationships between QCT-based apparent density of HVTB and its apparent compressive mechanical properties— elastic modulus (Eapp), yield strength (σy), and yield strain (εy)—in the SI and TR directions for future clinical QCT-based continuum finite element modeling of HVTB. A total of 51 cylindrical cores (33 axial and 18 transverse) were extracted from four L1 human lumbar cadaveric vertebrae. Intact vertebrae were scanned in a clinical resolution computed tomography (CT) scanner prior to specimen extraction to obtain QCT density, ρCT. Additionally, physically measured apparent density, computed as ash weight over wet, bulk volume, ρapp, showed significant correlation with ρCT [ρCT = 1.0568 × ρapp, r = 0.86]. Specimens were compression tested at room temperature using the Zetos bone loading and bioreactor system. Apparent elastic modulus (Eapp) and yield strength (σy) were linearly related to the ρCT in the axial direction [ESI = 1493.8 × (ρCT), r = 0.77, p < 0.01; σY,SI = 6.9 × (ρCT) − 0.13, r = 0.76, p < 0.01] while a power-law relation provided the best fit in the transverse direction [ETR = 3349.1 × (ρCT)1.94, r = 0.89, p < 0.01; σY,TR = 18.81 × (ρCT)1.83, r = 0.83, p < 0.01]. No significant correlation was found between εy and ρCT in either direction. Eapp and σy in the axial direction were larger compared to the transverse direction by a factor of 3.2 and 2.3, respectively, on average. Furthermore, the degree of anisotropy decreased with increasing density. Comparatively, εy exhibited only a mild, but statistically significant anisotropy: transverse strains were larger than those in the axial direction by 30%, on average. Ability to map apparent mechanical properties in the transverse direction, in addition to the axial direction, from CT-based densitometric measures allows incorporation of transverse properties in finite element models based on clinical CT data, partially offsetting the inability of continuum models to accurately represent trabecular architectural variations.


2005 ◽  
Vol 492-493 ◽  
pp. 555-560 ◽  
Author(s):  
L. Vandeperre ◽  
W.J. Clegg

The correlation between hardness, H, and yield strength, Y, for hard materials is reexamined using an analytical approach to provide a physical interpretation, which explains the trends observed. Existing analytical predictions using the analogy of the spherical cavity fail to reproduce experimental and finite element results because the accommodation of the intrusion of the indenter due to surface deformation is not taken into account, while experiments made here and elsewhere indicate that the latter can be substantial. A simple modification is proposed, which accounts for this, and allows for a reasonable prediction of the relation between hardness and yield strength for materials, which have a well determined yield point and do not strain harden. The treatment also allows explaining the effect of indenter geometry on measured hardness for such materials.


2004 ◽  
Vol 19 (12) ◽  
pp. 3704-3714 ◽  
Author(s):  
L.J. Vandeperre ◽  
F. Giuliani ◽  
W.J. Clegg

The use of an analytical approach to determine the relation between hardness and yield strength for materials with a high ratio of yield strength to Young's modulus is re-examined. It is shown that predictions using the analogy of the spherical cavity fail to reproduce experimental and finite element results because the surface deflection that occurs during loading is not taken into account. A modification is proposed to allow this. This gives a greatly improved prediction of the relationship between the hardness and yield strength of a material. It also enables the effect of the indenter shape on the measured hardness to be incorporated and explains why in some very hard materials, indentation is observed to be completely elastic.


2000 ◽  
Vol 649 ◽  
Author(s):  
Yang-Tse Cheng ◽  
Zhiyong Li ◽  
Che-Min Cheng

ABSTRACTUsing dimensional analysis and finite element calculations, the relationships between hardness, elastic modulus, final contact depth, and the work of indentation are extended to conical indentation in elastic-plastic solids with various cone angles. These relationships provide new insights into indentation measurements. They may also be useful to the interpretation of results obtained from instrumented indentation experiments.


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