- Email: [email protected]
Mechanical properties of ceramics–cement based porous material under impact loading
Materials and Design 55 (2014) 778–784
Contents lists available at ScienceDirect
Materials and Design journal homepage: www.elsevier.com/locate/matdes
Mechanical properties of ceramics–cement based porous material under impact loading q Luo Xin a,⇑, Xu Jin-yu a,b, Bai Er-lei a, Li Weimin c a
Department of Airfield and Building Engineering, Air Force Engineering University, Xi’an 710038, China College of Mechanics and Civil Architecture, Northwest Polytechnic University, Xi’an 710072, China c Airport Office, Air Force Logistics Department in Guangzhou Military Region, Guangzhou 510052, China b
a r t i c l e
i n f o
Article history: Received 29 June 2013 Accepted 16 October 2013 Available online 28 October 2013 Keywords: Porous material Impact mechanical properties Split Hopkinson pressure bar Impact mechanical properties Pulse shaping technique
a b s t r a c t Cementitious materials and ceramic aggregates used as basic materials, ceramics–cement based porous material (CCPM) has been prepared. U100 mm SHPB has been improved by wave shaping techniques, which can guarantee the availability of the tests. Quasi static compression test and impacting compression test have been carried out, the damage process of specimen under loading has been analyzed, and mechanics parameters under different strain rates have been obtained, moreover, based on this, the mechanical properties of CCPM under impact loading, including strength property, deformation property, impacting toughness, have been studied, in addition, the prospect of CCPM’s application has also been discussed. The results indicate that, the quasi static and impact compressive stress–strain curve of CCPM includes a strain plateau, which helps to better absorb energy; the dynamic strength increase factors of CCPM and the natural logarithm of relative strain rate are of a linear relationship; the relationship between the dynamic peak strain increase factors and the related strain rate can be described with an exponential linear, which shows obvious ‘‘damage softening’’ effect; with the increase of average strain rate, the impacting toughness of CCPM gets strengthened continuously and the impact toughness indexes are in a logarithm relationship with strain rate; CCPM is more strain rate sensitive than ordinary cement based composite materials. Thus it can be seen, CCPM possesses the advantageous mechanical properties of both porous materials and ordinary cement based composite materials. Besides, the material is easy to prepare and simple to make. Along with its high plasticity and low density, CCPM has a promising future to perform its potential advantages in engineering, especially in national defense engineering. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Porous material [1] is a net work system made up of the edges of holes and the walls beside them. It is widely seen in nature and widely used. Such materials include woods, bones, sponges, corals and so on. With their holes, porous materials [2] have great superiority over nonporous materials on noise reduction, heat protection, buffering and resisting impact. And the greatest advantage of porous materials is the mechanical properties, for they are compressible, have compress platform stress and their Poisson’s ratio is zero. With all the properties mentioned above, porous materials [3] have great advantages on strength, toughness and deformation.
q Foundation item: Projects of National Natural Science Foundation of China (51208507, 51078350); Projects of National Natural Science of Shaanxi province in China (2011gm6014). ⇑ Corresponding author. Tel.: +86 29 13630283725. E-mail addresses: [email protected], [email protected] (X. Luo).
0261-3069/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.matdes.2013.10.046
Currently, the studies on porous materials all around the world are mainly focused on the mechanical properties [4]. For example, Gibson and Silva [5] have made intensive researches on the mechanical properties of porous materials, where the properties have been analyzed, the materials’ deformation system has been visualized, its compressive mechanical model has been set up and the constitutive relations under the static state has been described. Besides, Mukai et al. [6] and some other researchers have studied the dynamic energy absorbing properties of closed-cell aluminum foam. Furthermore, Li-li [7] has theoretically and experimentally studied porous aluminum, hard foamed plastics and some other porous materials, analyzed the impacting properties of those materials and their transmission law of blast, and Wang et al. [8] presented an experimental investigation for the static and dynamic yield stresses of porous metals, especially, the influence of porosity on the dynamic yield stress of such materials under high loading rates is studied. It is clear that porous metals [9] and polymer-based composites [10] are the main porous materials applied in structure field. However, these kinds of material have many defects, like being hard to produce, being expensive,
779
X. Luo et al. / Materials and Design 55 (2014) 778–784
having low plasticity or low strength. So, it is very urgent to develop some new porous materials that do not have the defects mentioned above. In this paper, cementitious materials and ceramic aggregates have been used as basic materials. And based on Dense Packing Theory, ceramics–cement based porous material (CCPM) has been prepared. A quasi-static compression test of CCPM has been made with the help of improved HHY series electro-hydraulic servo system and the impact compression test has been made with the U100 mm SHPB improved by wave shaping techniques. After the tests, the mechanical parameters under different strain rates have been obtained. According to those data, the mechanical properties of CCPM under impact loading including strength properties, deformation properties and impact toughness have been analyzed, and the prospect of CCPM’s application has also been discussed. 2. Experimental details 2.1. Raw materials CCPM is made from cementitious materials and ceramic aggregates. Cementitious materials: cement: 42.5R PO, initial setting time is 2 h 10 min, final setting time is 5 h 10 min; fly ash: parameters reach the level of class I; silica fume: average particle size is among 0.1 0.15 lm, specific surface area is among 15 27 m2/g, SiO2 content is 92%; high efficiency slushing agent FDN: brown yellow powder, 20% water-reducing rate; water: drinking water. Ceramic aggregates: floating corundum bead: Al2O3 > 99%, compressive strength at normal temperature >8 Mpa ceramsite: packing density is 510 kg/m3, cylinder pressure strength P1.5 Mpa, water absorption 615%, shape coefficient is ‘‘globular shape 61.6’’. 2.2. Mixture ratio design The dense accumulation of particles system has great influence on many industrial fields and the core technique of it is how to apply Dense Accumulation Theory [11]. The fact that composite materials can be made from various raw materials makes it possible to apply the theory. Basic rules for mixture ratio design: firstly, test the packing density and apparent density of ceramisite aggregates, and make size analysis, making sure that the accumulated ceramisites are within the best gradation envelope. Artificial tamping experiment should be made to get the packing density and Lee’s Bottle Method should be used to get the apparent density. As for size analysis, it should be made in accordance with the envelopes. And the specific method in carrying our the packing density experiment on different alumina hollow ball aggregates is as follows: the vibration filling test on alumina hollow balls of different size levels should be made in accordance with the designed ratio. Stir the alumina hollow balls evenly and make sure they are fully mixed and fully filled so the packing density reaches the largest value and the mixture ratio of packing density is obtained. Secondly, fill the level matched alumina hollow balls of different sizes in ceramsites as instructed above, and the closely kitted framework is formed. Finally, pack three kinds of micro particles (cement, fly ash and micro-silica), so the biggest cement forms the frame, the smaller fly ash fills in the interspaces of cement and finally the smallest micro-silica fills in the interspaces between the closely knitted cement and fly ash. In this way, Solid-hole rate is significantly reduced, which increases van der Waals force between particles, and a new kind of high performance cementitious material is created. Paste is formed with cementitious material and water after dense
packing, the interspaces between framework-dense structures is filled with paste under some affluence coefficient, then target gradation which can be described as ‘‘minimum porosity, minimum specific surface area, and maximum packing density’’ is attained, finally dense packing CCPM is formed. The mixture ratio subjected to Dense Packing Theory is presented in every 1 m3 with 386 kg cement, 213.5 kg fly ash, 29.68 kg micro-silica, 5.93 kg FDN, 184 kg water, 352 kg ceramsite and 226 kg floating corundum bead. 2.3. Preparation method A 60 L forced mixer is used. Considering the characteristics of the materials, the alumina hollow balls and ceramsite should be mixed as follows. Mix up FDN and water up previously, and keep the these for the further usage. The mixing process: (1) stir the micro-silica and half amount of the cement for 30 s; (2) add three quarters of the prepared FDN and continue to stir for 30 s; (3) add the ceramsites and stir for another 30 s and (4) add the remaining FDN and cement, stir the mixture for another 120 s, and the uniform mixture is made. Put the mixture out of the mixer, and manually blend it while sprinkling the alumina hollow balls. The preparation of the specimen: in case of splice between the mixture and mould, the inner surface of the mould should be firstly coated with mineral oil. Put the ingredients in the mixer, and when the ingredients are fully mixed, put the mixture into the cylinder mould for shaping. The surface of the specimen should be covered with plastic wrap in case of water loss. Put the specimen in natural condition and remove it from the mould 24 h later. Right after the removal, maintain the specimen in standardized condition(T = 20 ± 2 °C, relative humanity >95%); 28 days later, polish the specimen (regulate the parallelity of the end faces and the surface flatness), and the geometric dimension of the specimen is about U95 50 mm, with a 1320 kg/m3 apparent density. Hole structures of CCPM specimen is shown in Fig. 1. The approach to form the hole structures is the key technology in the preparation of porous material, for CCPM, floating corundum beads with four parts of particle size level (0.2 1.0 mm, 1.0 2.0 mm, 2.0 3.0 mm, 3.0 mm 5.0 mm) are used, and the volume ratio of four parts is 73:9:10:8, which can guarantee the dense packing. 3. Quasi static mechanics testing A quasi-static compression test of CCPM is made with an improved electro-hydraulic servo system according to the Chinese national standards. Under different strain rates, to test the quasi static compression properties of CCPM, the loaded strain speeds
Fig. 1. Hole structures of CCPM.
780
X. Luo et al. / Materials and Design 55 (2014) 778–784
called incident pulse that propagates through the incident bar and reaches the interface of the incident bar–specimen. While some of the incident pulses is reflected back into the incident bar, the rest of them propagates through the specimen and generates the transmitted pulse in the transmitted bar. The test validity is mainly embodied in the Stress equilibrium and nearly constant strain rate loading. 4.2. Data processing
Fig. 2. Quasi static stress–strain curves of CCPM.
should be constant. The loaded strain speeds are 600 le= min; 6000 le= min and 12; 000 le= min; which can be converted into strain rates e_ , which are 1 105 s1, 1 104 s1, 2 104 s1 respectively. Under the quasi static state, the specimen directly enters elastic stage and some vertical or slanting cracks appear partially on the surface. As the strain gets higher, flaking phenomenon occurs partially and successively extends from the outside to the inside. As the flaking area gets greater, the heart is compressed continuously. When the loaded stress reaches a certain point, i.e. the limitation, the independent flaking areas gets connected, forming a wholly flaking surface and causing a complete damage to the specimen. After data processing, the stress–strain curves of CCPM under the quasi static state and three different strain rates are shown in Fig. 2. 4. Impact compressive testing 4.1. Basic introduction Split Hopkinson pressure bar (SHPB) [12] have been commonly employed to test metallic materials under compression at high strain rates, which has been developed for more than 60 years. Now the test technique has become more popular for the impact mechanical properties of many kinds of material [13]. A 100-mm-diameter SHPB is used in the impact compressive test, and this apparatus consists of main body, energy source and measurement system. The projectile, incident and transmission bars are made of 48CrMoA and have Young’s modulus of 210 GPa, density of 7850 kg/m3, and wave velocity of 5172 ms1. The schematic diagram is shown in Fig. 3. The basic principle of SHPB test is the propagation theory of elastic stress wave on the bar, and the test is based on the two following basic assumptions: (1) plane assumption; (2) stress equalizing assumption. The propagation process of stress pulse in the SHPB apparatus can be described as follows: the impact of the striker bar at the free end of the incident bar generates an elastic strain wave, which is
Incident pulse ei ; reflected pulse ei and transmitted pulse et can be recorded by using the strain gauge on the bar. Typical waves from the test are presented in Fig. 4. Based on the plane and stress equalizing assumption, and using the one-dimensional stress wave theory, the measurement data can be converted into strain rate (e_ s ðtÞ), stress (rs ðtÞ) and strain (es ðtÞ), which can be expressed respectively as follows:
9
> e_ s ðtÞ ¼ ðei elrset Þc > > > > = Eðei þer þet ÞA rs ðtÞ ¼ 2As R > es ðtÞ ¼ lcs 0t ðei er et Þds > > >
ð1Þ
> ;
where E is Young’s modulus of bar; c is wave velocity in bars; A and As are respectively the cross-sectional areas of bars and specimen, ls is the original length of the specimen. 4.3. Parameter control of testing technique In order to improve the accuracy of the dynamic mechanical properties test, pulse shaping technique [14] has been applied to the SHPB apparatus, and by means of parameter control, the incident pulse is shaped from square to half-sine-like, which can effectively reduce the dispersion effect and be beneficial to the dynamic stress equilibrium and nearly constant strain rate loading. 4.3.1. Dispersion effect The dispersion effect of square stress pulse produced by traditional SHPB apparatus is more obvious with the increase of bar diameter, so the dispersion effect [15] of U100 mm SHPB has a greater effect on test result. From the perspective of theoretical research, experimental research [16] and numerical simulation [17], some scholars have suggested that triangle-like or half-sine-like stress pulse can effectively reduce the dispersion effect. Fig. 5 presents typical incident wave under the different pulse shapers. As is shown in Fig. 6, wave oscillation is eliminated by using pulse shaping technique, and then the incident pulse fit for effectively reducing the dispersion effect is obtained. The reason is that in the process of impact loading, plastic deformation of shaper can effectively filter out the high frequency part of stress pulse, hence, the purpose of reducing dispersion effect can be reached.
Fig. 3. 100-mm-diameter SHPB system.
X. Luo et al. / Materials and Design 55 (2014) 778–784
Fig. 4. Typical waves from testing of CCPM.
781
Fig. 7. The curve of strain rate vs time.
R tR
Rt ðei þ er Þdt 0R et dt i. Rt R ðet þ er Þdt þ 0R et dt 2 0
dðtR Þ ¼ hR t
Fig. 5. Typical incident wave under the conditions of different pulse shapers.
0
ð2Þ
where tR is a specified action time of stress pulse. And the moment when d ¼ 5% can be defined as the moment when specimen achieves the stress equilibrium state (t u ¼ 58:05 ls). Compared with the failure time or the moment when specimen reaches the peak stress (t c ¼ 165:35 ls), when tc > tu, it can be accepted that specimen has achieved the stress equilibrium state before damaged. Take shaper with a 27 mm diameter as an example, stress equilibrium is analyzed, Fig. 6 presents the typical curve of stress equilibrium factor with time. Thus it can be seen, the stress equilibrium state is achieved before the failure of the specimen, besides, in most of the action time of stress pulse, the specimen is kept in a stable stress equilibrium state.
4.3.3. Nearly constant strain rate loading Nearly constant strain rate loading can be obtained by constantly adjusting two parameters, including the impact velocity (v) and shaper diameter (d). The average strain rate (e_ ) can be defined as the average value from achieving the stress equilibrium state to peak stress. Fig. 7 presents the curve of strain rate with time under different loading conditions, and corresponding e_ have also been found. As is shown in Fig. 7, the combination controlling with v and d had achieved the nearly constant strain rate loading, which can guarantee the validity of test and improve the its accuracy.
4.4. Testing result
Fig. 6. Typical curve of stress equilibrium factor with time.
4.3.2. Stress equilibrium It is easy to realize the stress equilibrium when studying the plastic materials, such as metals, with the SHPB apparatus, but for brittle materials, owing to the low wave velocity, the propagation time [18] of stress wave in specimen is long, and its failure strain is very small, usually only parts per thousand, so before the stress achieves an equilibrium state, the specimen has already been damaged in the ascent stage of square wave. Hence, stress equilibrium is a relatively big challenge. As is shown in Fig. 6, the rise time of shaped stress pulse is up to more than 200 ls, much bigger than the 69 ls of square stress pulse, thus it can provide sufficient time for the specimen to get to the stress equilibrium state. Stress equilibrium factor (d) can be defined as follows:
4.4.1. Damage forms Under impact effect, CCPM will go through a short compression stage and then enter the earlier elastic stage and earlier strain plateau stage. Later on, it will go back to elastic stage. When the impact gets close to the peak value, the specimen enters the plastic zone and the plastic deformation increases until it reaches the peak value. Then the plastic deformation decreases. When the plastic deformation decreases to some strain value, the specimen enters the later strain plateau stage. During whole process, the specimen goes with different forms of inner micro damage evolution, which finally causes the complete damage of the specimen. Typical facture morphology is shown in Fig. 8. According to Fig. 8, when the strain rate increases within the range of 10–150 s1, the damage forms of the specimen are as follows: unbroken, edge crack, edge broken, broken, and grinding. All forms of the damage actually do not occur suddenly, they are but a dynamic process that includes different forms of damage revolution and develops with a certain speed. After analyzing the damage
782
X. Luo et al. / Materials and Design 55 (2014) 778–784
(a) Unbroken
(b) Edge crake
(c) Edge broken
(d) Broken
(e) Grinding
Fig. 8. Typical facture morphology.
forms, it can be concluded that the damage degree of the specimen gets higher with the increase of strain rate. 4.4.2. Stress–strain curve The stress–strain curves of the impact compressive CCPM under different strain rate are obtained, as are shown in Fig. 9. According to Fig. 9, CCPM has the properties of both porous material and cement based composite material, i.e. it has strain plateau and shows Single peak phenomenon, from which it can be concluded that CCPM has advantages in strength and toughness. 5. Impacting mechanical properties The mechanical properties of a material include strength, deformation, toughness, energy features and so on. To make the analysis easier, pressure resisting strength is defined as the peak strain of some testing condition, which is the main strength indicator of the material. The quasi static pressure resisting strength is the peak stress fc,s the specimen reaches in the quasi static mechanical test; the compacting compression strength is peak stress fc,d the specimen reaches in the compacting compression test; and the peak strain ec is defined as the strain when the specimen reaches peak stress, which is the main deformation properties indicator of the material. 5.1. Strength properties For a more efficient analysis of the strength properties of CCPM, the Dynamic Increase Factor (DIF) of strength is defined as the ratio of the compacting compression strength to quasi static pressure resisting strength. It is an important indicator of the compressive strength increase level of material under the impact loading, as is expressed as follow:
DIF f ¼
fc;d fc;s
ð3Þ
Fig. 9. Stress–strain curve.
After some analysis, the changing law of DIFf with e_ is shown in formula (4).
( DIF f ¼
0:0966 ln e_ =e_ s þ 0:9323 105 6 e_ 6 48:00s1 0:7618 ln e_ =e_ s 9:2997 48:00 < e_ 6 150s1
ð4Þ
where e_ s is the universally accepted strain rate tested in the quasi static mechanical properties testing, and its value is 1 105 s1. CCPM’s strain rate sensitive threshold value e_ z;f is 48.00 s1. The strain rate sensitive threshold e_ z is set after repeated SHPB test and analysis of its critical phenomenon. On the one hand, e_ z;f is the critical strain rate of two of the five typical specimen damage forms: damage form (a) and damage form (b), on the other hand, under impact compression, after the average strain rate e_ z;f reaches the peak value, the stress–strain curve will not rebound once it reaches the peak point. Fig. 10 shows the change law of DIFf with ln e_ =e_ s . When the strain rates reach their specific strain rate thresholds, fc,d increases apparently and DIFf increases rapidly. On the inside of CCPM, there are dense micro-cracks and micro-holes of different sizes around the aggregate and throughout the cement slurry. The damage of concrete materials is the result of the formation and development of cracks, and it needs much more energy to form a crack than to develop a crack [19]. The faster the impacting speed is, the more cracks will be formed, and the more energy is in need. As the impacting time is very short, the material does not have enough time to absorb energy, that is to say, the deformation buffering is not effective. According to Theorem of Impulse or Work-energy Theorem, only by adding stress can offset the external impulse or energy. As a result, the damage degree of the material goes up with the increase of strain rate. Some scholars [20–22] have made systematic and penetrating researches on the dynamic mechanical properties of ordinary cement based composite material. Based on the analysis of a large number of experimental data, they proposed that when the strain rate is greater than some critical strain rate, the strength will increase largely and when the strain rate is within the range of
Fig. 10. The law between DIFf and ln e_ =e_ s .
783
X. Luo et al. / Materials and Design 55 (2014) 778–784
Fig. 12. The law between RP and e_ .
Fig. 11. The law between DIF f ;e and e_ =e_ s .
10–102 s1, the DIFf of cement based composite material can be expressed with a logarithm linear of average strain rate. The qualitative trend of CCPM’s strength properties is the same with that of ordinary cement based composite material, which indirectly verifies the accuracy of the test and shows that the two kinds of material share some characteristics in common. However, to a quantitative point of view, some differences can be detected, for the e_ z;f of ordinary cement based composite material is 63.1 s1, while the e_ z;f of CCPM is only 44.04 s1. So, it is clear that CCPM is more strain rate sensitive, which might have to give the credit to CCPM’s porous structure. With those porous structures, CCPM can express its overall strength properties better and faster. 5.2. Deformation properties To get to know the deformation properties of CCPM more efficiently, a dimensionless method should be applied in analyzing the variables. To better reflect the important indicators of the material’s stress increase level, the Dynamic Increase Factor (DIF f ;e ) of the peak value should be defined as the ratio of the ec when the specimen is in the impacting compression state to the ec when the specimen is in the quasi static compression state. As is expressed as follow:
of peak strain, so more energy is dissipated and the unstable expansion of the cracks is delayed, as a result, the specimen is softened and damaged during the loading process and brings about the increase of peak strain.
5.3. Impacting toughness Impacting toughness is the deformation capacity of a material when it is loaded with some stress, which is the combination of the material’s ductility and strength. From a macroscopic point of view, impacting toughness generally can be defined as the energy that a material or structure absorbs during the effective loading procedure. Impacting toughness is not only related to the strength of the material, but also depends on the strain of the material when it is damaged. As for how to scientifically evaluate impacting toughness, China applies some methods that are different from those of other countries. Generally speaking, there are two methods: one is by tenacity (RP), the area enclosed by the stress–strain curve and the strain axis; the other is by Specific Energy Absorption (SEA) [23], the physical interpretation of which is the stress wave energy every unit of the material absorbs. The second method takes many experimental factors into consideration, and the result is closer to the concrete value of the material’s impacting toughness. The expression is as follow:
SEA ¼
ec;d DIF f ;e ¼ ec;s
ð5Þ
Fig. 11 shows the changing law of DIFf,e with e_ =e_ s . After studying the figure, it can be concluded that DIFf,e shows obvious strain rate dependency; DIFf,e goes up with the increase of relative strain rate and the overall law fits in an exponential curve. See expression (6):
AEc As l s
Z
T
h
i
ei ðtÞ2 er ðtÞ2 et ðtÞ2 dt
where T is the moment when the specimen is completely damaged, and the other factors is as above.
DIF f ;e ¼ 1:04454e
1:04362107 _e_
es
ð6Þ
According to the expression, ec;d increases more largely as compared to ec;s . And according to the characteristics of exponential curves, the higher the strain rate is, the more sharply DIFf,e increases. This phenomenon is called ‘‘damage softening’’ effect [14]. The possible explanation [21] of this phenomena is that the formation and development of micro-cracks, micro holes and other damage forms soften the material; under impact loading effect, the damage evolutions inside the CCPM get exacerbated and the extension of massive micro-flaws produces damage process zone
ð7Þ
0
Fig. 13. The law between SEA and e_ .
784
X. Luo et al. / Materials and Design 55 (2014) 778–784
Two kinds of impacting toughness evaluating index are chosen to analyze CCPM. The changing laws of RP and SEA with average strain rate are respectively shown in Figs. 12 and 13. According to the figures, no matter adopting RP or SEA as the index, reached is the same conclusion where CCPM’s impacting toughness goes up continuously with the increase of average strain rate. On the one hand, it reflects the consistency and reasonableness of the two indexes, on the other hand, it testifies the reliability and stability of the result. The co-relationships are obtained by fitting, as is shown in formula 8.
(
RP ¼ 0:6536 þ 0:2489 lnðe_ 14:9681Þ R2 ¼ 0:9441 SEA ¼ 521:9660 þ 207:6087 lnðe_ 17:0747Þ R2 ¼ 0:9643 ð8Þ
This shows that impacting is in a logarithm relationship with e_ . With the increase of e_ , the acceleration of impacting toughness decreases to a certain value. 6. Conclusions The quasi static compression test and impacting compression test have been carried out; the mechanical properties of CCPM under impact loading, including strength property, deformation property, impacting toughness, have been analyzed. The main conclusions have been reached as follows: (1) Whether it is in the quasi static state or the impacting compression state, the stress–strain curve of CCPM includes a strain plateau, which helps to better absorbs energy. (2) The dynamic strength increase factors of CCPM and the natural logarithm of relative strain rate are of a linear relationship. (3) Under the impact compression state, the strain rate sensitive threshold for CCPM’s strength is e_ z;f ¼ 48:00 s1 . When strain rate is greater than e_ z;f , the impact compression intensity increases rapidly, the damages of the material change its form, and the stress–strain curve will not rebound once getting to the peak point. (4) Compared to ordinary cement based composite material, CCPM is more strain rate sensitive, which might have to give the credit to the porous structures. (5) The relationship between the dynamic peak strain increase factors and the related strain rate can be described with a exponential linear, which shows obvious ‘‘damage softening’’ effect. (6) With the increase of average strain rate, the impacting toughness of CCPM gets strengthened continuously and the impacting toughness indexes are in a logarithm relationship with e_ .
So, CCPM possesses the advantageous mechanical properties of porous material and ordinary cement based composite material. Besides, the material is easy to prepare and simple to make. Along with its high plasticity and low density, CCPM has a promising future to perform its potential advantages in engineering, especially in national defense engineering. References [1] Zhang Chunhua, Li Junqing, Zhen Hu, Zhu Fenglei, Huang Yudong. Correlation between the acoustic and porous cell morphology of polyurethane foam: effect of interconnected porosity. Mater Des 2012;41:319–25. [2] Gibson Lornal J, Ashby Michael F. Cellular solids: structure and properties. Beijing: Tsinghua University Press; 2003. p. 159–89 [in Chinese]. [3] Regleroa JA, Solórzanoa E, Rodríguez-Péreza MA, de Sajaa JA, Porrasb E. Design and testing of an energy absorber prototype based on aluminum foams. Mater Des 2010;31(7):3568–73. [4] Gan YX, Chen C, Shen YP. Three dimensional modeling of the mechanical property of elastomeric open cell foams. Int J Solids Struct 2005;42:6628–42. [5] Silva MJ, Gibson LJ. The effects of non-periodic microstructure and defects on the compressive strength of two-dimensional cellular solids. Int J Mech Sci 1997;39(5):549–63. [6] Mukai T, Kanahashi H, Miyoshi T, Mabuchi M, Nieh TG, Higashi K. Experimental study of energy absorption in a close-celled aluminum foam under dynamic loading. Scripta Mater 1999;40(8):921–7. [7] Li-li Wang. Progress in studies on dynamics response of structures and materials under explosive/impact loading. Explo Shock Waves 2001;21(2):81–8 [in Chinese]. [8] Wang B, Zhang J, Lu G. Taylor impact test for ductile porous materials. Part 2: experiments. Int J Impact Eng 2003;28(5):499–511. [9] Cho Jae Ung, Hong Soon Jik, Lee Sang Kyo, et al. Impact fracture behavior at the material of aluminum foam. Mater Sci Eng: A 2012;539:250–8. [10] Kasparek Eva, Zencker Uwe, Scheidemann Robert, et al. Numerical and experimental studies of polyurethane foam under impact loading. Comput Mater Sci 2011;50(4):1353–8. [11] Vandamme Matthieu, Ulm Franz-Josef, Fonollosa Philip. Nano granular packing of C–S–H at substochiometric conditions. Cem Concr Res 2010;40(1):14–26. [12] Kolsky H. An investigation of the mechanical properties of materials at very high rates of loading. Proc Phys Soc London 1949;62(II-B):676–700. [13] Li WM, Xu JY. Impact characterization of basalt fiber reinforced geopolymeric concrete using a 100-mm-diameter split Hopkinson pressure bar. Mater Sci Eng: A 2009;513–514:145–53. [14] Frew DJ, Forrestal MJ, Chen W. Pulse shaping techniques for testing brittle materials with a split Hopkinson pressure bar. Exp Mech 2002;42(1):93–106. [15] Pochhammer L. On the velocity of propagation of small vibrations in an isotropic cylinder of infinite length. J fur d& Reineund Angew Math (Crelle) 1876;81:324–36. [16] LI Xibing, GU Desheng. Rock impact dynamics. Changsha: Central South University of Technology Press; 1994 [in Chinese]. [17] Luo Xin Xu, Jinyu Li Weimin, Jun Zhang. Numerical simulation and spectral analysis of dispersion effect of stress pulse in SHPB tests. J Exp Mech 2010;25(4):451–6 [in Chinese]. [18] Ravichandran G, Subhash G. Critical appraisal of limiting strain rates for compression testing of ceramics in a split hopkinson pressure bar. Am Ceram Soc 1994;77(1):263–7. [19] Wang Daorong, Hu Shisheng. Influence of aggregate on the compression properties of concrete under impact. J Exp Mech 2002;17(1):23–7 [in Chinese]. [20] Ross CA, Tedesco JW, Kuennen ST. Effects of strain-rate on concrete strength. ACI Mater J 1995;92(1):37–47. [21] Ross CA, Jerome DM, Tedesco JW, Hughes ML. Moisture and strain rate effects on concrete strength. ACI Mater J 1996;93(3):293–300. [22] Tedesco JW, Ross CA, Kuennen ST. Experimental and numerical analysis of high strain rate splitting tensile test s. ACI Mater J 1993;90(2):162–9. [23] Yu Tong-xi, Lu Guo-xing. Energy absorption of material and construction. Beijing: Chemical Industry Press; 2005 [in Chinese].
Contents lists available at ScienceDirect
Materials and Design journal homepage: www.elsevier.com/locate/matdes
Mechanical properties of ceramics–cement based porous material under impact loading q Luo Xin a,⇑, Xu Jin-yu a,b, Bai Er-lei a, Li Weimin c a
Department of Airfield and Building Engineering, Air Force Engineering University, Xi’an 710038, China College of Mechanics and Civil Architecture, Northwest Polytechnic University, Xi’an 710072, China c Airport Office, Air Force Logistics Department in Guangzhou Military Region, Guangzhou 510052, China b
a r t i c l e
i n f o
Article history: Received 29 June 2013 Accepted 16 October 2013 Available online 28 October 2013 Keywords: Porous material Impact mechanical properties Split Hopkinson pressure bar Impact mechanical properties Pulse shaping technique
a b s t r a c t Cementitious materials and ceramic aggregates used as basic materials, ceramics–cement based porous material (CCPM) has been prepared. U100 mm SHPB has been improved by wave shaping techniques, which can guarantee the availability of the tests. Quasi static compression test and impacting compression test have been carried out, the damage process of specimen under loading has been analyzed, and mechanics parameters under different strain rates have been obtained, moreover, based on this, the mechanical properties of CCPM under impact loading, including strength property, deformation property, impacting toughness, have been studied, in addition, the prospect of CCPM’s application has also been discussed. The results indicate that, the quasi static and impact compressive stress–strain curve of CCPM includes a strain plateau, which helps to better absorb energy; the dynamic strength increase factors of CCPM and the natural logarithm of relative strain rate are of a linear relationship; the relationship between the dynamic peak strain increase factors and the related strain rate can be described with an exponential linear, which shows obvious ‘‘damage softening’’ effect; with the increase of average strain rate, the impacting toughness of CCPM gets strengthened continuously and the impact toughness indexes are in a logarithm relationship with strain rate; CCPM is more strain rate sensitive than ordinary cement based composite materials. Thus it can be seen, CCPM possesses the advantageous mechanical properties of both porous materials and ordinary cement based composite materials. Besides, the material is easy to prepare and simple to make. Along with its high plasticity and low density, CCPM has a promising future to perform its potential advantages in engineering, especially in national defense engineering. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Porous material [1] is a net work system made up of the edges of holes and the walls beside them. It is widely seen in nature and widely used. Such materials include woods, bones, sponges, corals and so on. With their holes, porous materials [2] have great superiority over nonporous materials on noise reduction, heat protection, buffering and resisting impact. And the greatest advantage of porous materials is the mechanical properties, for they are compressible, have compress platform stress and their Poisson’s ratio is zero. With all the properties mentioned above, porous materials [3] have great advantages on strength, toughness and deformation.
q Foundation item: Projects of National Natural Science Foundation of China (51208507, 51078350); Projects of National Natural Science of Shaanxi province in China (2011gm6014). ⇑ Corresponding author. Tel.: +86 29 13630283725. E-mail addresses: [email protected], [email protected] (X. Luo).
0261-3069/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.matdes.2013.10.046
Currently, the studies on porous materials all around the world are mainly focused on the mechanical properties [4]. For example, Gibson and Silva [5] have made intensive researches on the mechanical properties of porous materials, where the properties have been analyzed, the materials’ deformation system has been visualized, its compressive mechanical model has been set up and the constitutive relations under the static state has been described. Besides, Mukai et al. [6] and some other researchers have studied the dynamic energy absorbing properties of closed-cell aluminum foam. Furthermore, Li-li [7] has theoretically and experimentally studied porous aluminum, hard foamed plastics and some other porous materials, analyzed the impacting properties of those materials and their transmission law of blast, and Wang et al. [8] presented an experimental investigation for the static and dynamic yield stresses of porous metals, especially, the influence of porosity on the dynamic yield stress of such materials under high loading rates is studied. It is clear that porous metals [9] and polymer-based composites [10] are the main porous materials applied in structure field. However, these kinds of material have many defects, like being hard to produce, being expensive,
779
X. Luo et al. / Materials and Design 55 (2014) 778–784
having low plasticity or low strength. So, it is very urgent to develop some new porous materials that do not have the defects mentioned above. In this paper, cementitious materials and ceramic aggregates have been used as basic materials. And based on Dense Packing Theory, ceramics–cement based porous material (CCPM) has been prepared. A quasi-static compression test of CCPM has been made with the help of improved HHY series electro-hydraulic servo system and the impact compression test has been made with the U100 mm SHPB improved by wave shaping techniques. After the tests, the mechanical parameters under different strain rates have been obtained. According to those data, the mechanical properties of CCPM under impact loading including strength properties, deformation properties and impact toughness have been analyzed, and the prospect of CCPM’s application has also been discussed. 2. Experimental details 2.1. Raw materials CCPM is made from cementitious materials and ceramic aggregates. Cementitious materials: cement: 42.5R PO, initial setting time is 2 h 10 min, final setting time is 5 h 10 min; fly ash: parameters reach the level of class I; silica fume: average particle size is among 0.1 0.15 lm, specific surface area is among 15 27 m2/g, SiO2 content is 92%; high efficiency slushing agent FDN: brown yellow powder, 20% water-reducing rate; water: drinking water. Ceramic aggregates: floating corundum bead: Al2O3 > 99%, compressive strength at normal temperature >8 Mpa ceramsite: packing density is 510 kg/m3, cylinder pressure strength P1.5 Mpa, water absorption 615%, shape coefficient is ‘‘globular shape 61.6’’. 2.2. Mixture ratio design The dense accumulation of particles system has great influence on many industrial fields and the core technique of it is how to apply Dense Accumulation Theory [11]. The fact that composite materials can be made from various raw materials makes it possible to apply the theory. Basic rules for mixture ratio design: firstly, test the packing density and apparent density of ceramisite aggregates, and make size analysis, making sure that the accumulated ceramisites are within the best gradation envelope. Artificial tamping experiment should be made to get the packing density and Lee’s Bottle Method should be used to get the apparent density. As for size analysis, it should be made in accordance with the envelopes. And the specific method in carrying our the packing density experiment on different alumina hollow ball aggregates is as follows: the vibration filling test on alumina hollow balls of different size levels should be made in accordance with the designed ratio. Stir the alumina hollow balls evenly and make sure they are fully mixed and fully filled so the packing density reaches the largest value and the mixture ratio of packing density is obtained. Secondly, fill the level matched alumina hollow balls of different sizes in ceramsites as instructed above, and the closely kitted framework is formed. Finally, pack three kinds of micro particles (cement, fly ash and micro-silica), so the biggest cement forms the frame, the smaller fly ash fills in the interspaces of cement and finally the smallest micro-silica fills in the interspaces between the closely knitted cement and fly ash. In this way, Solid-hole rate is significantly reduced, which increases van der Waals force between particles, and a new kind of high performance cementitious material is created. Paste is formed with cementitious material and water after dense
packing, the interspaces between framework-dense structures is filled with paste under some affluence coefficient, then target gradation which can be described as ‘‘minimum porosity, minimum specific surface area, and maximum packing density’’ is attained, finally dense packing CCPM is formed. The mixture ratio subjected to Dense Packing Theory is presented in every 1 m3 with 386 kg cement, 213.5 kg fly ash, 29.68 kg micro-silica, 5.93 kg FDN, 184 kg water, 352 kg ceramsite and 226 kg floating corundum bead. 2.3. Preparation method A 60 L forced mixer is used. Considering the characteristics of the materials, the alumina hollow balls and ceramsite should be mixed as follows. Mix up FDN and water up previously, and keep the these for the further usage. The mixing process: (1) stir the micro-silica and half amount of the cement for 30 s; (2) add three quarters of the prepared FDN and continue to stir for 30 s; (3) add the ceramsites and stir for another 30 s and (4) add the remaining FDN and cement, stir the mixture for another 120 s, and the uniform mixture is made. Put the mixture out of the mixer, and manually blend it while sprinkling the alumina hollow balls. The preparation of the specimen: in case of splice between the mixture and mould, the inner surface of the mould should be firstly coated with mineral oil. Put the ingredients in the mixer, and when the ingredients are fully mixed, put the mixture into the cylinder mould for shaping. The surface of the specimen should be covered with plastic wrap in case of water loss. Put the specimen in natural condition and remove it from the mould 24 h later. Right after the removal, maintain the specimen in standardized condition(T = 20 ± 2 °C, relative humanity >95%); 28 days later, polish the specimen (regulate the parallelity of the end faces and the surface flatness), and the geometric dimension of the specimen is about U95 50 mm, with a 1320 kg/m3 apparent density. Hole structures of CCPM specimen is shown in Fig. 1. The approach to form the hole structures is the key technology in the preparation of porous material, for CCPM, floating corundum beads with four parts of particle size level (0.2 1.0 mm, 1.0 2.0 mm, 2.0 3.0 mm, 3.0 mm 5.0 mm) are used, and the volume ratio of four parts is 73:9:10:8, which can guarantee the dense packing. 3. Quasi static mechanics testing A quasi-static compression test of CCPM is made with an improved electro-hydraulic servo system according to the Chinese national standards. Under different strain rates, to test the quasi static compression properties of CCPM, the loaded strain speeds
Fig. 1. Hole structures of CCPM.
780
X. Luo et al. / Materials and Design 55 (2014) 778–784
called incident pulse that propagates through the incident bar and reaches the interface of the incident bar–specimen. While some of the incident pulses is reflected back into the incident bar, the rest of them propagates through the specimen and generates the transmitted pulse in the transmitted bar. The test validity is mainly embodied in the Stress equilibrium and nearly constant strain rate loading. 4.2. Data processing
Fig. 2. Quasi static stress–strain curves of CCPM.
should be constant. The loaded strain speeds are 600 le= min; 6000 le= min and 12; 000 le= min; which can be converted into strain rates e_ , which are 1 105 s1, 1 104 s1, 2 104 s1 respectively. Under the quasi static state, the specimen directly enters elastic stage and some vertical or slanting cracks appear partially on the surface. As the strain gets higher, flaking phenomenon occurs partially and successively extends from the outside to the inside. As the flaking area gets greater, the heart is compressed continuously. When the loaded stress reaches a certain point, i.e. the limitation, the independent flaking areas gets connected, forming a wholly flaking surface and causing a complete damage to the specimen. After data processing, the stress–strain curves of CCPM under the quasi static state and three different strain rates are shown in Fig. 2. 4. Impact compressive testing 4.1. Basic introduction Split Hopkinson pressure bar (SHPB) [12] have been commonly employed to test metallic materials under compression at high strain rates, which has been developed for more than 60 years. Now the test technique has become more popular for the impact mechanical properties of many kinds of material [13]. A 100-mm-diameter SHPB is used in the impact compressive test, and this apparatus consists of main body, energy source and measurement system. The projectile, incident and transmission bars are made of 48CrMoA and have Young’s modulus of 210 GPa, density of 7850 kg/m3, and wave velocity of 5172 ms1. The schematic diagram is shown in Fig. 3. The basic principle of SHPB test is the propagation theory of elastic stress wave on the bar, and the test is based on the two following basic assumptions: (1) plane assumption; (2) stress equalizing assumption. The propagation process of stress pulse in the SHPB apparatus can be described as follows: the impact of the striker bar at the free end of the incident bar generates an elastic strain wave, which is
Incident pulse ei ; reflected pulse ei and transmitted pulse et can be recorded by using the strain gauge on the bar. Typical waves from the test are presented in Fig. 4. Based on the plane and stress equalizing assumption, and using the one-dimensional stress wave theory, the measurement data can be converted into strain rate (e_ s ðtÞ), stress (rs ðtÞ) and strain (es ðtÞ), which can be expressed respectively as follows:
9
> e_ s ðtÞ ¼ ðei elrset Þc > > > > = Eðei þer þet ÞA rs ðtÞ ¼ 2As R > es ðtÞ ¼ lcs 0t ðei er et Þds > > >
ð1Þ
> ;
where E is Young’s modulus of bar; c is wave velocity in bars; A and As are respectively the cross-sectional areas of bars and specimen, ls is the original length of the specimen. 4.3. Parameter control of testing technique In order to improve the accuracy of the dynamic mechanical properties test, pulse shaping technique [14] has been applied to the SHPB apparatus, and by means of parameter control, the incident pulse is shaped from square to half-sine-like, which can effectively reduce the dispersion effect and be beneficial to the dynamic stress equilibrium and nearly constant strain rate loading. 4.3.1. Dispersion effect The dispersion effect of square stress pulse produced by traditional SHPB apparatus is more obvious with the increase of bar diameter, so the dispersion effect [15] of U100 mm SHPB has a greater effect on test result. From the perspective of theoretical research, experimental research [16] and numerical simulation [17], some scholars have suggested that triangle-like or half-sine-like stress pulse can effectively reduce the dispersion effect. Fig. 5 presents typical incident wave under the different pulse shapers. As is shown in Fig. 6, wave oscillation is eliminated by using pulse shaping technique, and then the incident pulse fit for effectively reducing the dispersion effect is obtained. The reason is that in the process of impact loading, plastic deformation of shaper can effectively filter out the high frequency part of stress pulse, hence, the purpose of reducing dispersion effect can be reached.
Fig. 3. 100-mm-diameter SHPB system.
X. Luo et al. / Materials and Design 55 (2014) 778–784
Fig. 4. Typical waves from testing of CCPM.
781
Fig. 7. The curve of strain rate vs time.
R tR
Rt ðei þ er Þdt 0R et dt i. Rt R ðet þ er Þdt þ 0R et dt 2 0
dðtR Þ ¼ hR t
Fig. 5. Typical incident wave under the conditions of different pulse shapers.
0
ð2Þ
where tR is a specified action time of stress pulse. And the moment when d ¼ 5% can be defined as the moment when specimen achieves the stress equilibrium state (t u ¼ 58:05 ls). Compared with the failure time or the moment when specimen reaches the peak stress (t c ¼ 165:35 ls), when tc > tu, it can be accepted that specimen has achieved the stress equilibrium state before damaged. Take shaper with a 27 mm diameter as an example, stress equilibrium is analyzed, Fig. 6 presents the typical curve of stress equilibrium factor with time. Thus it can be seen, the stress equilibrium state is achieved before the failure of the specimen, besides, in most of the action time of stress pulse, the specimen is kept in a stable stress equilibrium state.
4.3.3. Nearly constant strain rate loading Nearly constant strain rate loading can be obtained by constantly adjusting two parameters, including the impact velocity (v) and shaper diameter (d). The average strain rate (e_ ) can be defined as the average value from achieving the stress equilibrium state to peak stress. Fig. 7 presents the curve of strain rate with time under different loading conditions, and corresponding e_ have also been found. As is shown in Fig. 7, the combination controlling with v and d had achieved the nearly constant strain rate loading, which can guarantee the validity of test and improve the its accuracy.
4.4. Testing result
Fig. 6. Typical curve of stress equilibrium factor with time.
4.3.2. Stress equilibrium It is easy to realize the stress equilibrium when studying the plastic materials, such as metals, with the SHPB apparatus, but for brittle materials, owing to the low wave velocity, the propagation time [18] of stress wave in specimen is long, and its failure strain is very small, usually only parts per thousand, so before the stress achieves an equilibrium state, the specimen has already been damaged in the ascent stage of square wave. Hence, stress equilibrium is a relatively big challenge. As is shown in Fig. 6, the rise time of shaped stress pulse is up to more than 200 ls, much bigger than the 69 ls of square stress pulse, thus it can provide sufficient time for the specimen to get to the stress equilibrium state. Stress equilibrium factor (d) can be defined as follows:
4.4.1. Damage forms Under impact effect, CCPM will go through a short compression stage and then enter the earlier elastic stage and earlier strain plateau stage. Later on, it will go back to elastic stage. When the impact gets close to the peak value, the specimen enters the plastic zone and the plastic deformation increases until it reaches the peak value. Then the plastic deformation decreases. When the plastic deformation decreases to some strain value, the specimen enters the later strain plateau stage. During whole process, the specimen goes with different forms of inner micro damage evolution, which finally causes the complete damage of the specimen. Typical facture morphology is shown in Fig. 8. According to Fig. 8, when the strain rate increases within the range of 10–150 s1, the damage forms of the specimen are as follows: unbroken, edge crack, edge broken, broken, and grinding. All forms of the damage actually do not occur suddenly, they are but a dynamic process that includes different forms of damage revolution and develops with a certain speed. After analyzing the damage
782
X. Luo et al. / Materials and Design 55 (2014) 778–784
(a) Unbroken
(b) Edge crake
(c) Edge broken
(d) Broken
(e) Grinding
Fig. 8. Typical facture morphology.
forms, it can be concluded that the damage degree of the specimen gets higher with the increase of strain rate. 4.4.2. Stress–strain curve The stress–strain curves of the impact compressive CCPM under different strain rate are obtained, as are shown in Fig. 9. According to Fig. 9, CCPM has the properties of both porous material and cement based composite material, i.e. it has strain plateau and shows Single peak phenomenon, from which it can be concluded that CCPM has advantages in strength and toughness. 5. Impacting mechanical properties The mechanical properties of a material include strength, deformation, toughness, energy features and so on. To make the analysis easier, pressure resisting strength is defined as the peak strain of some testing condition, which is the main strength indicator of the material. The quasi static pressure resisting strength is the peak stress fc,s the specimen reaches in the quasi static mechanical test; the compacting compression strength is peak stress fc,d the specimen reaches in the compacting compression test; and the peak strain ec is defined as the strain when the specimen reaches peak stress, which is the main deformation properties indicator of the material. 5.1. Strength properties For a more efficient analysis of the strength properties of CCPM, the Dynamic Increase Factor (DIF) of strength is defined as the ratio of the compacting compression strength to quasi static pressure resisting strength. It is an important indicator of the compressive strength increase level of material under the impact loading, as is expressed as follow:
DIF f ¼
fc;d fc;s
ð3Þ
Fig. 9. Stress–strain curve.
After some analysis, the changing law of DIFf with e_ is shown in formula (4).
( DIF f ¼
0:0966 ln e_ =e_ s þ 0:9323 105 6 e_ 6 48:00s1 0:7618 ln e_ =e_ s 9:2997 48:00 < e_ 6 150s1
ð4Þ
where e_ s is the universally accepted strain rate tested in the quasi static mechanical properties testing, and its value is 1 105 s1. CCPM’s strain rate sensitive threshold value e_ z;f is 48.00 s1. The strain rate sensitive threshold e_ z is set after repeated SHPB test and analysis of its critical phenomenon. On the one hand, e_ z;f is the critical strain rate of two of the five typical specimen damage forms: damage form (a) and damage form (b), on the other hand, under impact compression, after the average strain rate e_ z;f reaches the peak value, the stress–strain curve will not rebound once it reaches the peak point. Fig. 10 shows the change law of DIFf with ln e_ =e_ s . When the strain rates reach their specific strain rate thresholds, fc,d increases apparently and DIFf increases rapidly. On the inside of CCPM, there are dense micro-cracks and micro-holes of different sizes around the aggregate and throughout the cement slurry. The damage of concrete materials is the result of the formation and development of cracks, and it needs much more energy to form a crack than to develop a crack [19]. The faster the impacting speed is, the more cracks will be formed, and the more energy is in need. As the impacting time is very short, the material does not have enough time to absorb energy, that is to say, the deformation buffering is not effective. According to Theorem of Impulse or Work-energy Theorem, only by adding stress can offset the external impulse or energy. As a result, the damage degree of the material goes up with the increase of strain rate. Some scholars [20–22] have made systematic and penetrating researches on the dynamic mechanical properties of ordinary cement based composite material. Based on the analysis of a large number of experimental data, they proposed that when the strain rate is greater than some critical strain rate, the strength will increase largely and when the strain rate is within the range of
Fig. 10. The law between DIFf and ln e_ =e_ s .
783
X. Luo et al. / Materials and Design 55 (2014) 778–784
Fig. 12. The law between RP and e_ .
Fig. 11. The law between DIF f ;e and e_ =e_ s .
10–102 s1, the DIFf of cement based composite material can be expressed with a logarithm linear of average strain rate. The qualitative trend of CCPM’s strength properties is the same with that of ordinary cement based composite material, which indirectly verifies the accuracy of the test and shows that the two kinds of material share some characteristics in common. However, to a quantitative point of view, some differences can be detected, for the e_ z;f of ordinary cement based composite material is 63.1 s1, while the e_ z;f of CCPM is only 44.04 s1. So, it is clear that CCPM is more strain rate sensitive, which might have to give the credit to CCPM’s porous structure. With those porous structures, CCPM can express its overall strength properties better and faster. 5.2. Deformation properties To get to know the deformation properties of CCPM more efficiently, a dimensionless method should be applied in analyzing the variables. To better reflect the important indicators of the material’s stress increase level, the Dynamic Increase Factor (DIF f ;e ) of the peak value should be defined as the ratio of the ec when the specimen is in the impacting compression state to the ec when the specimen is in the quasi static compression state. As is expressed as follow:
of peak strain, so more energy is dissipated and the unstable expansion of the cracks is delayed, as a result, the specimen is softened and damaged during the loading process and brings about the increase of peak strain.
5.3. Impacting toughness Impacting toughness is the deformation capacity of a material when it is loaded with some stress, which is the combination of the material’s ductility and strength. From a macroscopic point of view, impacting toughness generally can be defined as the energy that a material or structure absorbs during the effective loading procedure. Impacting toughness is not only related to the strength of the material, but also depends on the strain of the material when it is damaged. As for how to scientifically evaluate impacting toughness, China applies some methods that are different from those of other countries. Generally speaking, there are two methods: one is by tenacity (RP), the area enclosed by the stress–strain curve and the strain axis; the other is by Specific Energy Absorption (SEA) [23], the physical interpretation of which is the stress wave energy every unit of the material absorbs. The second method takes many experimental factors into consideration, and the result is closer to the concrete value of the material’s impacting toughness. The expression is as follow:
SEA ¼
ec;d DIF f ;e ¼ ec;s
ð5Þ
Fig. 11 shows the changing law of DIFf,e with e_ =e_ s . After studying the figure, it can be concluded that DIFf,e shows obvious strain rate dependency; DIFf,e goes up with the increase of relative strain rate and the overall law fits in an exponential curve. See expression (6):
AEc As l s
Z
T
h
i
ei ðtÞ2 er ðtÞ2 et ðtÞ2 dt
where T is the moment when the specimen is completely damaged, and the other factors is as above.
DIF f ;e ¼ 1:04454e
1:04362107 _e_
es
ð6Þ
According to the expression, ec;d increases more largely as compared to ec;s . And according to the characteristics of exponential curves, the higher the strain rate is, the more sharply DIFf,e increases. This phenomenon is called ‘‘damage softening’’ effect [14]. The possible explanation [21] of this phenomena is that the formation and development of micro-cracks, micro holes and other damage forms soften the material; under impact loading effect, the damage evolutions inside the CCPM get exacerbated and the extension of massive micro-flaws produces damage process zone
ð7Þ
0
Fig. 13. The law between SEA and e_ .
784
X. Luo et al. / Materials and Design 55 (2014) 778–784
Two kinds of impacting toughness evaluating index are chosen to analyze CCPM. The changing laws of RP and SEA with average strain rate are respectively shown in Figs. 12 and 13. According to the figures, no matter adopting RP or SEA as the index, reached is the same conclusion where CCPM’s impacting toughness goes up continuously with the increase of average strain rate. On the one hand, it reflects the consistency and reasonableness of the two indexes, on the other hand, it testifies the reliability and stability of the result. The co-relationships are obtained by fitting, as is shown in formula 8.
(
RP ¼ 0:6536 þ 0:2489 lnðe_ 14:9681Þ R2 ¼ 0:9441 SEA ¼ 521:9660 þ 207:6087 lnðe_ 17:0747Þ R2 ¼ 0:9643 ð8Þ
This shows that impacting is in a logarithm relationship with e_ . With the increase of e_ , the acceleration of impacting toughness decreases to a certain value. 6. Conclusions The quasi static compression test and impacting compression test have been carried out; the mechanical properties of CCPM under impact loading, including strength property, deformation property, impacting toughness, have been analyzed. The main conclusions have been reached as follows: (1) Whether it is in the quasi static state or the impacting compression state, the stress–strain curve of CCPM includes a strain plateau, which helps to better absorbs energy. (2) The dynamic strength increase factors of CCPM and the natural logarithm of relative strain rate are of a linear relationship. (3) Under the impact compression state, the strain rate sensitive threshold for CCPM’s strength is e_ z;f ¼ 48:00 s1 . When strain rate is greater than e_ z;f , the impact compression intensity increases rapidly, the damages of the material change its form, and the stress–strain curve will not rebound once getting to the peak point. (4) Compared to ordinary cement based composite material, CCPM is more strain rate sensitive, which might have to give the credit to the porous structures. (5) The relationship between the dynamic peak strain increase factors and the related strain rate can be described with a exponential linear, which shows obvious ‘‘damage softening’’ effect. (6) With the increase of average strain rate, the impacting toughness of CCPM gets strengthened continuously and the impacting toughness indexes are in a logarithm relationship with e_ .
So, CCPM possesses the advantageous mechanical properties of porous material and ordinary cement based composite material. Besides, the material is easy to prepare and simple to make. Along with its high plasticity and low density, CCPM has a promising future to perform its potential advantages in engineering, especially in national defense engineering. References [1] Zhang Chunhua, Li Junqing, Zhen Hu, Zhu Fenglei, Huang Yudong. Correlation between the acoustic and porous cell morphology of polyurethane foam: effect of interconnected porosity. Mater Des 2012;41:319–25. [2] Gibson Lornal J, Ashby Michael F. Cellular solids: structure and properties. Beijing: Tsinghua University Press; 2003. p. 159–89 [in Chinese]. [3] Regleroa JA, Solórzanoa E, Rodríguez-Péreza MA, de Sajaa JA, Porrasb E. Design and testing of an energy absorber prototype based on aluminum foams. Mater Des 2010;31(7):3568–73. [4] Gan YX, Chen C, Shen YP. Three dimensional modeling of the mechanical property of elastomeric open cell foams. Int J Solids Struct 2005;42:6628–42. [5] Silva MJ, Gibson LJ. The effects of non-periodic microstructure and defects on the compressive strength of two-dimensional cellular solids. Int J Mech Sci 1997;39(5):549–63. [6] Mukai T, Kanahashi H, Miyoshi T, Mabuchi M, Nieh TG, Higashi K. Experimental study of energy absorption in a close-celled aluminum foam under dynamic loading. Scripta Mater 1999;40(8):921–7. [7] Li-li Wang. Progress in studies on dynamics response of structures and materials under explosive/impact loading. Explo Shock Waves 2001;21(2):81–8 [in Chinese]. [8] Wang B, Zhang J, Lu G. Taylor impact test for ductile porous materials. Part 2: experiments. Int J Impact Eng 2003;28(5):499–511. [9] Cho Jae Ung, Hong Soon Jik, Lee Sang Kyo, et al. Impact fracture behavior at the material of aluminum foam. Mater Sci Eng: A 2012;539:250–8. [10] Kasparek Eva, Zencker Uwe, Scheidemann Robert, et al. Numerical and experimental studies of polyurethane foam under impact loading. Comput Mater Sci 2011;50(4):1353–8. [11] Vandamme Matthieu, Ulm Franz-Josef, Fonollosa Philip. Nano granular packing of C–S–H at substochiometric conditions. Cem Concr Res 2010;40(1):14–26. [12] Kolsky H. An investigation of the mechanical properties of materials at very high rates of loading. Proc Phys Soc London 1949;62(II-B):676–700. [13] Li WM, Xu JY. Impact characterization of basalt fiber reinforced geopolymeric concrete using a 100-mm-diameter split Hopkinson pressure bar. Mater Sci Eng: A 2009;513–514:145–53. [14] Frew DJ, Forrestal MJ, Chen W. Pulse shaping techniques for testing brittle materials with a split Hopkinson pressure bar. Exp Mech 2002;42(1):93–106. [15] Pochhammer L. On the velocity of propagation of small vibrations in an isotropic cylinder of infinite length. J fur d& Reineund Angew Math (Crelle) 1876;81:324–36. [16] LI Xibing, GU Desheng. Rock impact dynamics. Changsha: Central South University of Technology Press; 1994 [in Chinese]. [17] Luo Xin Xu, Jinyu Li Weimin, Jun Zhang. Numerical simulation and spectral analysis of dispersion effect of stress pulse in SHPB tests. J Exp Mech 2010;25(4):451–6 [in Chinese]. [18] Ravichandran G, Subhash G. Critical appraisal of limiting strain rates for compression testing of ceramics in a split hopkinson pressure bar. Am Ceram Soc 1994;77(1):263–7. [19] Wang Daorong, Hu Shisheng. Influence of aggregate on the compression properties of concrete under impact. J Exp Mech 2002;17(1):23–7 [in Chinese]. [20] Ross CA, Tedesco JW, Kuennen ST. Effects of strain-rate on concrete strength. ACI Mater J 1995;92(1):37–47. [21] Ross CA, Jerome DM, Tedesco JW, Hughes ML. Moisture and strain rate effects on concrete strength. ACI Mater J 1996;93(3):293–300. [22] Tedesco JW, Ross CA, Kuennen ST. Experimental and numerical analysis of high strain rate splitting tensile test s. ACI Mater J 1993;90(2):162–9. [23] Yu Tong-xi, Lu Guo-xing. Energy absorption of material and construction. Beijing: Chemical Industry Press; 2005 [in Chinese].