Investigation of the Hygrothermal Effect on the Nanocomposite Material under High Strain Rate Torsion

This study aims to explain the effect of high strain rate torsion on unidirectional fiber glass / epoxy composite with and without adding nano particles (carbon and alumina) with weight percentage 2% and study the effect of the temperature and humidity on the samples under torsion dynamic test. Using the torsional Hopkinson split bar to testing under angle of the twist θ=10°. It can noticed that the maximum of the shear (stress, strain) of the composite increased with adding nano particles by rate of (24.8%, 3.2%) with added 2% nano carbon and (26%, 8.5%) with added 2% nano alumina, where the shear stress, shear strain and shear strain rate of all samples decreased with increasing (temperature and humidity) with different percentages. Finally, it was modifying Johnson-Cook constitutive model by adding parameter represented the humidity effect to simulate the experimental results, and then it was found the error percentages between the experimental results and theoretical results which range (0.0044% and 15.5%).


Introduction
In a lot of engineering applications the materials loaded at strain rate from quasi-static loading which ranges 10 −5 s −1 to dynamic loading at strain rate 10 3 s −1 while the hydraulic machines which used normally to testing material at strain rates up to 5 s −1 [1]. The split Hopkinson pressure bar (SHPB) device is using to make high strain rate that involve strain rate range (10 2 to 10 4 ) s −1 for testing material. Materials pass in high strain rates deformation in different applications, e.g. engineering applications such as bullet proof armor, has crashed worthiness of vehicles, impact resistant pressure vessel and events such as penetrations, explosions and penetrations. In addition to forming processes as rolling, extrusion, and high speed machining can also lead in high strain rate deformation [2,3] for have the better design and safety analysis of element is required testing the material at high strain rate NASA John H. Glenn (2003) [4] studied the effect of strain rate on mechanical response of three types of epoxy resins. The experimental results progress the information needed for NASA scientists to development which can hgfgh98`1 then it be used in the design. using a torsional split Hopkinson bar to testing three types of epoxy resins (PR-520, E-862 and 977-2 ) under shear stress at different strain rates with ranges (5x10 −5 to 2 and 400 to 1000) −1 and the temperature testing used at room temperature and 80°C. The results shown that all the strain rate used and temperatures significantly effect on the response of epoxy and the maximum shear stress decrease when the temperature increased and increased with increased strain rate for all resins, for example the shear stress increased from 48 Mpa to 85 Mpa when the strain rate increased from 1.3x10 −4 −1 to 700 −1 for E-862. M. Nabil Bassim (2012) [5] used torsional split Hopkinson bar to test high strength steel with high strain rates .The specimen was forming from thin walls with two hexagonal ends. The specimens tested at different angles of twists, the samples were tested at the many angles of twist (10°, 8°, 4°, 1.5°) at room temperature. One of the samples testing at 10° angle of twist under temperature 500°C and 200°C. The result given that the shear (stress, strain) increased with increased angle of the twist and shear stress decreased with increased temperature at the same angle of twist 10°. Also using Johnson cook to simulation the result based on the experimental test. Ali Majid Ibraheem (2015) [6] using split Hopkinson Pressure bar (SHPB) in compression test with thermal effect. Used epoxy resin and fiber-glass / epoxy composite and added three types of nano particles were carbon black (N220), alumina ( 2 3) and s-glass. The nano particles added with different weight fraction 2% and 4%. It used two different temperature to test samples were at room temperature and 150°C. The result showed 9 that the dynamic stress and strain decreased with temperature 150 °C while increased with addition nano particles to fiber-glass/epoxy composite where the nano particles improved the values of strain rate, strain, stress .In the end adding 4% nano particle (carbon black, alumina and s-glass) to composite material improved strain rate, strain, stress greater than addition 2% nano particles. Finally used Johnson Cook model in the theoretical analysis to simulation the experimental work, where it was found error percentages less 15%.the aim of this study focused on 1.

Material Properties
In present work the composite material content from fiber glass and epoxy resin (Sikadur 52) and nano particle (alumina and carbon black) as shown in figures(1,2,3), so in Table (1) shows the properties of epoxy resin ,Table (2) shows list of the properties of fiberglass and Table (3) Properties of Nanoparticle which were used in the experimental work.

Preparation of Samples
Several steps have been taken to manufacture samples as below:

Determined the Weight Fraction of Fiber
The weight fraction of specimen that used in the test is =25%. The details are shown in the table (4)

Specimen Geometry
The specimen used with specific dimensions as shown in figure (4).

Molding and Cutting
Consist from many steps which is 1. used glass mold cylindrical shape with opened end to molding the specimen have the dimensions (internal diameter and a length 18 mm, 150mm respectively ,Lubricating the inner walls of the mold with material adhesion blocker then the fiber glass with are arranged in the mold in the homogenous as shown in figure (5).

Added nano particles to epoxy (after weight them )
then mixed manually at 25 c° for (3 to10) minutes until the mixture become homogeneous in glass box as shown in figure (6) then Adding the hardener to the epoxy-nano mixture then mixing good by hand as shown in figure (7). the mixing with ratio (2:1) by using the mixer for 10 minutes by slowly to mix the mixture as shown in figure (8), finally Using ultrasonic device to eliminate the existing void in the mixture for 5 minutes as shown in figure (9) 3. The mixture poured into the mold to filling the mold and leaves from 24 to 48 hours to solidification then the samples are cut by using lathe machine on the shape as shown figure (10).

Dynamic Test
In this study is used split Hopkinson torsion bar to test the samples with high strain rates. The split Hopkinson torsion bar consist from incident bar, transmitted bar, Clamp system, Support Block (Brackets), Adapters, Torque Generating Mechanism, End Fixing, Bushing and steel channel [8], so it used measurement system that consist from two couple of strain gage which bonded in incident band transmitted bar then connected to Wheatstone bridge that connect with digital oscilloscope finally connect the digital oscilloscope with personal computer ( laptop ) as shown in figure (11) To provide different environmental conditions to study effect environmental conditions (temperature and humidity) was used accelerated weathering chamber [9] where the samples are placed for five hours under the effect of heat and humidity is different as shown in the table (5) after the samples are tested with split Hopkinson torsion apparatus bar with angle of twist 10°.

Static Test
The compression test give information about properties of material tested (stress and strain). The shape and the dimensions of specimen was tested accord to (ASTM-D695M-89) standards [10] , where Lo do ⁄ ratios are 1.5 to 3 therefore used specimen with diameter 18 mm and length 36 mm shown figure (15) In this test the specimens tested by using compression test machine (TINIUS OLSEN H50KT) as shown in figure (16)

Calculation Shear Stress, Strain-Rate, Strain of the Specimen
Calculated the shear strain rate, shear strain and shear stress from the elastic wave signals that was captured in incident, transmitted and reflected waves by use two couples of strain gage using equations [5]:

Johnson-Cook Constitutive Model and the suggestion of Modification Johnson-Cook Constitutive Mode
Constitutive model that describes the flow stress depending on strain, strain rate and temperature, to the simulations of deformation at high strain rate used The five-parameter experimental Johnson-Cook (JC) constitutive model [10].The model represents The Johnson-Cook constitutive relation is represent Where Єp : it is represented the plastic strain equivalently .
A: it is represented the yield stress which correspond to 0.2% displacement (offset) strain. The constant A is determined from the stress-strain curve where it is plotted an offset 0.2% strain at strain rate ~1/s. B and n: represented the strain hardening effects of the material. They are determined from plotted the Logarithmic plastic strain vs. plastic strain.
C: it is represented the strain rate effect (strain rate sensitivity).It is determined as slope the linear of Ln (strain rate) vs. (Dynamic stress/ Static stress). And ε̇ * = ε/ε̇ °, Where ε̇ ° is the reference strain-rate (static strain rate ) and ̇ is the strain-rate of sample at testing T * : it is represented the homologous temperature = ( T test − T ROOM ) /(T MELT − T ROOM ) where m : it is represented thermal effect and is determined from plotted of the relation between Ln (T * ) and Ln(1 heating / ) for thermal effect and on the condition of ε= ̇ ° and Єp = 0.
The first expression of brackets was represented the stress in terms of strain when ̇ * =1.0 and T* = 0. The second and third expression of brackets was represented the strain rate and temperature effects respectively through constant c, m and k [11]. Details will be clarified in chapter five.
The von Mises yield criterions are used to convert the shear stress into equivalent stress using the relations before used it in Johnson-Cook Constitutive model [12]:

Dynamic Tests Results
In figure (17) to (28), it can be seen that the shear stress and shear strain decreased with increased temperature and humidity with different percentage and the shear strain rate decreased with increased temperature and humidity that explained in table (6) 14 Investigation of the Hygrothermal Effect on the Nanocomposite Material under High Strain Rate Torsion

Static Tests Results for All Groups of Materials
The theoretical model based on (Johnson-Cook equation) using the static compression test results to calculate the constant of (Johnson-Cook equation) to comparing between the theoretical and experimental results. The value of the maximum strain and stress of material from static tests were shown in table (7).

Analytical Assessment of Results (The equation of Johnson -Cook)
The dynamic shear test results for all groups of tested materials by using Johnson-cook constitutive model. It was used the Johnson-Cook constitutive model to specify the theoretical stress-strain behavior for G4 in all condition. Depended on Johnson-Cook constitutive model, the following equation "(9)," can obtain for G3 depended on equation "(4),": To explain the effect of humidity (moisture content ) on G4 where it has been modified Johnson-cook constitutive model and added a new part representing the effect of moisture [1-H * K ],at the condition (strain rate of ~ 1/s, When Є = 0 , the room temperature) where the equation "(9)," in the form : The  The relation between LnH * and Ln (1 humidity / RH) can be plotted to evaluate (k) as shown in figure (30).

Discussion
The results shown that the shear (stress, strain , strain rate ) of G2 and G3 at TrHr more than shear (stress, strain , strain rate) of G1 where they increased with added 2% nano carbon and nano alumina with percentage ( 24.91 %, 3.2 %, 10.56 %) and (26.31%, 8.5%, 16%) respectively because the nano particles are improved the mechanical and physical properties of the composite so the bonded between atoms became stronger because added nano particles caused increased the interference between the epoxy and nano particles which lead to reduce the movement of polymer [13].so shown that the shear properties (stress, strain ,strain rate) decreased with increasing temperature and humidity of all groups of materials ,where it can be seen in behavior of G1 that the shear stress at (TrHr) decreased by rate of 14.03% with increased temperature to 100C° at (T100Hr) and (TrHr) decreased by rate of 12.4% with increased humidity ratio to 90% at (TrH90) so the decreased percentage increasing when increased temperature and humidity ratio together ,where dynamic shear stress of (TrHr) decreased by 21.05%with increased temperature to T100 and increased humidity to 90% at (T100H90) because the increasing of the humidity and temperature reduce the properties and increase the movement of the molecules of the composite caused decreasing the bonded between the fiber and matrix ,in addition the high temperature caused leads to increased moisture content Subsequently the substance becomes weaker.

Investigation of the Hygrothermal Effect on the Nanocomposite Material under High Strain Rate Torsion
In the second groups G2 (composite with 2% nano carbon) behaves the same behavior as the composite material under the effect of temperature and humidity but it decreased with different rates where the dynamic shear stress of TrHr decreased by 11.73% with increased temperate to 100C° at (T100Hr) , G2 at (TrHr) decreased by rate of 11.4% with increased humidity ratio to 90% at (TrH90) and decreased by 23.8% with increased temperature to T100 and increased humidity to 90% at (T100H90). finally the dynamic shear stress at (TrHr) of G3 decreased by rate of 13.88% with increased temperature to 100C° and 13% with increased humidity to 90 while the dynamic shear stress decreased by 25.3% at T100H90. In all cases with increased temperature and humidity all materials behaves the same behavior .in addition decreased dynamic shear stress because temperature and humidity the shear strain and shear strain rate decreased with different percentage as shown in table (6).

Conclusions
It can be seen that the conclusions as below: 1. For three groups ( unidirectional fiber glass/ epoxy composite, unidirectional fiber glass/ epoxy composite with 2% nano carbon , unidirectional fiber glass/ epoxy composite with 2% nano alumina and unidirectional fiber glass/) can be observed in the results of the shear dynamic test that the maximum of the shear strain and shear strain rate increased with increasing shear stress. 2. The results shown that the dynamic shear (stress, strain, strain rate) increased with add nano particles. 3. The results of the second group (composite with 2% nano carbon) shown good improvement in the shear properties of fiber glass/epoxy composite after added nano carbon ,where the dynamic shear stress of composite increased by 24.91%. 4. The results of the group (composite with 2% nano alumina) and shown best improvement in the shear properties of fiber glass/epoxy composite when added nano alumina , because the nano alumina composite have the best properties, where the dynamic shear stress of composite increased by 26.31% 5. All group of materials affected by ( temperature and humidity ) and the fiber glass/epoxy composite was more effected than others where the shear stress and shear strain as shear stress decreased with increased temperature or humidity ,so the effect was greater with increased temperature and humidity together (hygrothermal effect) and the effect of the temperature was higher than the humidity. 6. Added nano particle increased the strength of composite under hygrothermal effect. 7. Used Johnson-Cook equation and modified to clarify the effect of the humidity by add new parameter (k) and found the constants A, B, C, n ,finally it can be used the modification on Johnson-Cook model with a reasonable percentage error. 8. It can be seen the reasonable percentage error between the results which obtained from Johnson-Cook constitutive model (theoretical method) 00 and experimental method.