| Because of favorably physical and mechanical properties, ceramics are widely used for the lightweight armor-defended materials. As typical brittle materials, ceramics are highly sensitive to the deformation, and completely distinguished from the damage and failure behavior of ductile materials. Under impact process, ceramics experience crack or fragment caused by serious damage, and hence the state of damaged and broken regime directly influences their capability of defense (anti-penetration) usage.This paper is primarily devoted to the study of alumina ceramics through the combination with experimental and theoretical analyses. We systematically investigated the compressive damage form and discipline of alumina AD95under the shock loading stress range from0.5GPa to57.4GPa. The study shows:(a) when the shock loading stress is less than a threshold, which is less than the HEL, the material does not exhibit compressive damage and its spall strength gradually increases with the loading stress;(b) when the loading stress is larger than the threshold, which is still less than the HEL, however, AD95demonstrates a compressive damage and the residual spall strength decreases rapidly. As the loading stress reaches HEL, AD95completely loses the spall strength;(c) when the loading stress is over the HEL, the material starts to produce an equivalent damage, which leads to the gradual reduction of high-pressure sound velocity and effective shear modulus at the Hugoniot state;(d) when the loading stress is higher than about40GPa, the material becomes a state with seriously equivalent damage and likes as a quasi-liquid. Nevertheless, due to the friction effect among the broken grains under compressive stress, the high-pressure sound velocity decreases but not degrades to be the bulk sound velocity, and the effective shear modulus also reduces but not decreases to be zero, which indicates that the material remains to have an apparent strength.Following is the main content and conclusion of this study:1. Shock compressive damage at low-stress regionThe oxygen-free copper flyer with enough thickness accelerated by one-stage light gas gun impacts with AD95ceramic target, and the particle velocity profile at the free surface of target is measured through the VISAR technique under the one-dimensional plane strain shock compression. On the basis of characterized analysis about the velocity profile and theoretical analysis combined with fracture and damage mechanics, we demonstrate: (1) In a shock stress range from4.4GPa to7.3GPa (HEL is about5.5GPa), the free surface velocity profile has no appearance of two-times loading signal, which means that there is no appearance of the seriously damaged and fragmentized interface as that observed in glass and rock, like as a failure wave.(2) The analysis about the free surface velocity profile indicates that the calculated characterizing time difference is disciplinarily less than the experimental value, and the rising foreland has a dispersive property even though the loading stress is less than HEL. These findings demonstrate that, to some extent, AD95ceramics might have produced a certain weak compressive damage at the low-stress region.(3) Based on the theoretical analysis of fracture mechanics, the compressive damage process is related to the extension of microcracks, which are controlled by the fracture toughness and microscopic structure of material, except for the loading stress and loading time. Materials with relatively lower fracture toughness are proned to form microcracks extension, connection and finally lead to the serious breakage and shatter into pieces. Besides, the configuration and distribution of microcracks in the body of material is also a significant ingredient that affects the failure behavior.2. Residual spall strength at low-stress regionThe experimental approach on spall strength at low-stress region is conducted by a thin flyer impacting into a relatively thick AD95ceramic target. The particle velocity profile at the free surface of target or the interface between target and window is measured through the DISAR technique. By analyzing the characteristic of velocity profile, the residual spall strength of sample is calculated, which is then used for evaluating the shock compressive damage and its variation as a function of loading stress. The primary results are:(1) The relationship between the residual spall strength and the loading stress is:(2) The threshold value of loading stress with the occurrence of shock compressive damage for AD95ceramics is about3.7GPa, which is less than its HEL (about5.5GPa), validating that to some extent the compressive damage surely occurs under the shock loading less than HEL, and also shows that HEL is not the critical point for the compressive damage. (3) The shock compressive damage enhances with the increase of loading stress. When the loading stress reaches the HEL, the residual spall strength of AD95falls down to zero, which illustrates that the material has a relatively severe compressive damage for tensile stress. Additionally, once the loading stress is larger than the threshold, the spall strength distributes scatterly, reflecting that the sample indeed yields some extent of compressive damage.(4) Theoretical analysis of fracture mechanics indicates:for the shock loading stress less than3.5GPa, the stress intensity factor Ki is wholly less than the fracture toughness of material KIC and the microcracks within the material would not extend, confirming that the compressive damage in sample does not occur; for the shock stress of3.5-3.8GPa, the distributed regime of KI and KIC overlaps, indicating that part of the microcracks within the sample begin to propagate and the compressive damage happens, which consistents with the threshold stress of compressive damage about3.7GPa obtained from the spall strength measurement; as the loading stress continues increasing, the compressive damage also becomes severe. Once the loading stress reaches the HEL or above, KI is larger than KIC, which means that a great amount of microcracks within the sample will spread and the material reaches the relatively serious compressive damage state. Such a fracture mechanics analysis is in accord well with the compressive damage analysis characterized by spall strength measurement.(5) The results about the shock compressive damage characterized by residual spall strength explain and demonstrate very well the conclusion that failure wave in the AD95ceramics could not be observed.3. Shock compressive damage at high-pressure regionThrough the head-on and reverse impacted methods, we have measured the high-pressure sound velocity and unloading path of AD95ceramics at the stress range of5.9-57.4GPa. Utilizing the DISAR technique with window, the particle velocity profile at the interface of ceramic sample and LiF window has been measured during the loading and unloading processes. Based on these results, we calculated the Lagrange sound velocity of ceramic sample at the initial shock compressed state and unloading process, and obtained the unloading path. Through the analysis of unloading character and mechanism, and the relationship of the high-pressure sound velocity changing with the loading stress, we have characterized the compressive damage state and its degree of AD95ceramics at the relatively high-pressure shock loading. The main conclusions are as the follows: (1) AD95ceramics has a novel characteristic unloading process obviously differing from that of the ductile material:Firstly, the unloading process is continuously changing and has no apparently transitioning point between elastic and plastic unloading. Secondly, under different loading stress, for the ductile material the unloading segments almost converge to the same path, while for AD95ceramics, it exists a certain distance in the non-elastic unloading portion and the stress and engineering strain along the unloading path is apparently deviated from the Hugoniot curve. Such a unique characteristic of unloading process implies that the unloading mechanism is much different between AD95ceramics and ductile metal. We conjecture that the unloading process in AD95ceramics is governed by the broken grains produced by the compressive stress loading and reflects the information of compressive damage in the loading process.(2) We proposed a concept of the equivalent damage that implies the reduction of high-pressure sound velocity caused by the compressive damage. The variation between the sound velocity and the shock pressure (or stress) is:at the low loading state (the stress is less than HEL), the measured sound velocity is basically along the theoretical curve of the longtitudinal sound velocity without damage, which indicates that AD95ceramics does not yet produce an equivalent damage or a little; for the loading stress larger than HEL, the sound velocity is gradually less than the theoretical longtitudinal sound velocity, illustrating that the equivalent damage occurs; as the loading stress increases more, the sound velocity decreases more and gradually approaches to the theoretical value of bulk sound velocity, meaning that the equivalent damage constantly increases with the shock loading stress; when the loading stress reaches from30to40GPa, the sound velocity does not go to the theoretical bulk sound velocity any longer but goes parallelly and higher than it. This result may mean that the shear modulus of AD95ceramics could not reduce to zero if it has not melted yet. We realize that AD95ceramics remains an apparent strength after the serious damage, which confirms the suggestion that the compressive state is controlled by the friction effect among the broken grains inside the material.(3) By defining the equivalent damage parameter as D=(CI-CIH)/(CI-Cb), we demonstrate the increment of the equivalent damage with the shock stress, and it shows the characteristic of "S" shape. When the loading stress is less than HEL, D≈0, meaning that the equivalent damage does not occur; once the loading stress is larger than HEL, the value of D gradually increases, from the beginning of about20GPa, D rapidly rises up; when the loading stress reaches above30-40GPa, the rising rate of D becomes slower, the value of D equilibrates to about0.67. (4) The theoretical analysis of fracture mechanics shows:for the loading stress in the vicinity of HEL, the KI is slightly larger than the KIC, indicating that microcracks start to extend; as the loading stress further increases, the KI continuously increases, which causes the continuous increase of the number of microcracks in terms of nucleation and propagation in the shocked AD95ceramics, and makes the damage more heavy.(5) We obtained new and deep understanding about the meaning of HEL for polycrystalline alumina ceramics:HEL is not the transition point from elastic to plastic deformation as well as not the critical point of shock compressive damage, but a critical point where the shock compressive damage has the response to or has the effect on the propagation of stress wave, therefore HEL is the threshold value that the equivalent compressive damage begins. Seen from the microscopic mechanism, HEL is the transition point where the damage mechanism type (e.g. changing from a small amount of cracks along the crystalline direction to a great amount of cracks traversing the crystal) and damage extent transform from the quantitative to the qualitative.4. The residual shear modulus at high-pressure regionThe shear modulus at the Hugoniot state is an indication of material strength, containing the information of compressive damage under the shock loading. The findings of this study of high-pressure sound velocity for AD95ceramics indicate:(1) Compared with the theoretical shear modulus, the residual shear modulus has the apparent dropdown process when the loading stress is larger than the HEL, which illustrates that AD95ceramics starts to produce equivalent damage and the degree of damage constantly increases;(2) Though the residual shear modulus decreases but not reduce to zero, AD95ceramics has still some apparent strength even at high-pressure region;(3) When the loading stress is larger than about40GPa, the residual shear modulus gradually enhances, but is obviously less than the theoretical shear modulus. Besides, the residual shear modulus almost goes parallelly to the theoretical shear modulus, which indicates that AD95ceramics has yielded severe damage and located at a quasi-liquid like state. |
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