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(a) α= 0.0 0.0 0.1 0.2 0.3 0.4 0.5 RELATIVE CRACK DEPTH, ξ = a / D 0.0 1.0 2.0 3.0 α= -1.0 TENSION Present Study Caspers et al.
Results by Caspers et al. [20] are also reported. 0.0 0.1 0.2 0.3 0.4 0.5 RELATIVE CRACK DEPTH, ξ = a / D 0.0 1.0 2.0 3.0 K*I(M) = KI(M) / σI(M) (πa)1/2 α= -1.0 BENDING Present Study Caspers et al.
Results by Caspers et al. [20] are also reported.
( )( ) ( ) ( )( ) 121 2 21 2 = − + + + i el i el a Dy b x (8) where D is the bar diameter; (3) The crack has a straight front.
Salah el din and J.M.

Artzner et al. (1999) firstly introduced the concept of coherent risk measure, by proposing four basic properties to be satisfied by every sound financial risk measure.
However, the cash additive axiom has been criticized from an economic viewpoint.Cash additivity fails as soon as there is any form of uncertainty about interest rates.For this reason EL Karoui and Ravanelli (2009) suggest to replace cash additivity with cash subadditivity.
The multivariate analogue of the Value-at-Risk discussed by Embrechts and Puccetti (2006) is based on set-valued quantiles of the multivariate cumulative distribution function.Jouini et al.(2004) and Kulikov (2008) defined multidimensional risk measures as set-valued functional,and they proved the corresponding representation results.
EL Karoui and Ravanelli (2009) replaced cash additivity with cash subadditivity, named cash subadditivity risk measure.
[4]EL Karoui N, Ravanelli C.

The electroluminescence (EL) spectra were obtained by a spectrometer (SM442) connected with fiber optic wire.
Metz et al. reported high ionization energies of iron oxide and copper oxide compared to the iron and copper metals, respectively [26].
To analyze the effect of Ag nanoparticles on the peaks shift in EL spectra of OLED devices, Fig. 4 presents the normalized EL of reference device and OLED with Ag nanoparticles.
The normalized EL showed no shift in the wavelength of the spectra peaks for all devices, which is around 497 nm, as shown in the inset figure.
Al-Masoodi, N.F.F.B.

Yasam et al. (2016) developed nifedipine loaded niosomes for the transdermal treatment of hypertension.
El Maghraby et al. (2015) in their study reported the preparation of proniosomes for nisoldipine transdermal delivery.
Al-Japairai et al., “Current trends in polymer microneedle for transdermal drug delivery,” Int.
Al-Japairai, and S.
El Maghraby, A.

Petit el. al [40], measured the nonlinear refractive index (n2) of new germanium-based sulfo-selenide glasses by using Z-scan technique at 1064 nm, with picosecond pulses emitted by a 10 Hz Q-switched mode-locked Nd:Yag laser.
Murgan el al. [42] added WO3 (up to 10 mol%) and P2O5 (up to 16 mol%) in TeO2–BaO–SrO–Nb2O5 (TBSN) glass system and studied thermal and optical properties of the doped glasses.
[8] R El Mallawnay, J.
Al- Ani, C., Hogarth, J.
El Diasty, J.

Mamalis el al. [2] experimentally investigated on low-carbon steel St37, medium carbon steel C45 and alloyed steel 100Cr6 work piece and found that the peak stresses are almost independent of the discharge energy and approach the ultimate tensile strength of the material.
Rebelo el al. [3] in his investigation using XRD methodology found that the residual stress of steel work piece increases from the bulk material to a maximum and decreases again approaching the surface.
A qualitative relationship with the operating parameters was presented by Ekmekci el al. [4] using DIN 1.2738 (AISI P20) work piece material.
Yadav et al. [5] applied FEM to investigate the thermal stress generated by a single spark in EDM of Cr die steel.
Marafona et al. [6] developed a thermal-electrical model for sparks generated by electrical discharge in a liquid media.

The second possibility is substituting for cement, Aliabdo et al. found a positive effect on the mechanical properties of mortar and concrete when they substituting marble powder per the cement.
Ibrahim, et al., Health Risk Assessment of Marble Dust at Marble Workshops, Nature and Science, 9 (2011) 144-154
El-Hefnawi, Characterization of The Marble Sludge of The Shaq El Thoaban Industrial Zone, Egypt and Its Compatibility for Various Recycling Applications 6 (2012) 153-161
Prošek, et al., Influence of recycled concrete composition on its elastic stiffness, Key Engineering Materials 677 (2016) 288-291
Topič et al., Effect of PVA modification on the properties of cement composites, Acta Polytechnica 55 (2015) 64-75.

Le et al. [6] used 2-D graphene nanoplatelets (GNPs) in cement composites for structural health evaluation.
Zhou Fan et al. [7] investigated the properties of cementitious materials reinforced by graphene.
El-Gamal, S.
Abo-El-Enein, F.
El-Hosiny, M.

Some modification to its formulation were performed by Duncan et al [3-4].
Fig. 1a shows the obtained curves of axial strain el vs deviation stress (s1-s3), Fig 1b shows the curves of axial strain el vs the volume strain ev, and Fig. 1c shows the series of Mohr circles.
s 1-s 3 (kPa) e1 Fig. 1a Curves of Axial Strain e1 vs Deviation Stress stress (s1-s3) ev e1 Fig. 1b Curves of Axial Strain el vs Volume Strain ev τ (kPa) s ( kPa) Fig. 1c Mohr Circles c=22 (kPa) and f=33.8 (deg) were obtained from Mohr circles.
el/(σ1-σ3) el Fig.2 Relationship between εl/(σ1-σ3) and εl The intercept and the slope of the straight lines in Fig2 are 1/Ei and 1/(σ1-σ3)ult respectively.
This means the value of tangent modulus essentially the tangent modulus when strain is very small, say to the magnitude of 10-6 as Duncan et al mentioned[3,6,7].

HPTed Ti [4], ECAPed Armco-iron [5], low-carbon steel [6], Al [7], Cu [4,8], ARBed Al alloy. [9] Among SPD techniques, HPT process is one of the most powerful techniques to prepare ultrafine-grained (UFG) materials owing to non-homogeneous deformation with large strain and large strain gradient. [10-12] The principle of HPT-straining bases on the procedure developed by Bridgman. [13] A thin disk is placed between two anvils and subjected to torsional straining under a high pressure.
The ultimate tensile strength, UTS, and the total elongation, EL, were plotted in Fig. 8 as a function of number of turns.
It is also noteworthy that the EL increased with strain from εeq = 45 to εeq = 91 (number of turns from N = 5 to 10) and attained around 30 % in the HPT-processed specimen for N = 10, as shown in Fig. 8 (b).
The large EL and the increase in it with strain seem to be explained with the enhancement of recovery due to the larger fraction of high-angle grain boundaries [32] and the reduction of the stress concentration by the existence of grains with low dislocation density [8].
Fig. 6 Thermal stability of Hv at the region of r = 4 mm after HPT-straining for N = 5 (εeq = 121). 2) The Hv in the HPT-processed submicrocrystalline Fe attained around Hv 3.6 GPa. 3) The UTS and the EL of the HPT-processed Fe for N = 5 and 10 were 1.9 GPa, 20 % and 1.9 GPa, 30 %, respectively.