APPLICATION OF THE SINGLE IMPACT MICROINDENTATION FOR NON- DESTRUCTIVE TESTING OF THE FRACTURE TOUGHNESS OF NONMETALLIC AND POLYMERIC MATERIALS

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1 APPLICATION OF THE SINGLE IMPACT MICROINDENTATION FOR NON- DESTRUCTIVE TESTING OF THE FRACTURE TOUGHNESS OF NONMETALLIC AND POLYMERIC MATERIALS REN A. P. INSTITUTE OF APPLIED PHYSICS OF THE NATIONAL ACADEMY OF SCIENCE Mink Belaru At preent time the technical progre give new requirement to engineering material and thi lead to gradual replacement of metal with polymer and compoite. Mot intenively thi proce occur in the automobile and aviation indutry and pecialit evaluate that by 00 their part in the element of load-bearing tructure will reach 40-50%. In thi connection it become neceary to evaluate the propertie of uch material not only at their manufacture but alo during exploitation. One of the mot important parameter of the material reponible for it exploitation reliability i fracture toughne. A a rule fracture toughne i determined on pecially produced ample. For material and product of mall ize uch method are inapplicable beide they alo do not allow to perform control of real product. The bet olution in thi cae i application of indentation and analyi of crack formed at intruion of axiymmetric indenter into the material. In thi connection a tak ha been et in thi paper to determine applicability of the indentation method for evaluation of fracture toughne for elatoplatic polymer material and for polymethyl methacrylate (PMMA) in particular. The ample of PMMA type TOSP- ha been elected a tet object. Thi material i optically tranparent which allow to trace the proce of fracture. Indentation wa carried out in the tatic and dynamic mode. Static loading wa performed on the Vicker hardne meter. The hardne meter wa additionally equipped with LED enor which allowed to meaure hardne at loading a well a after it removal. Meauring of the intruion depth wa conducted with preciion of 10 µm. In the dynamic mode the material i loaded by indenter that fall free at the moment of impact. At the ame time the device pecially deigned for thee purpoe allowed to record not only the final parameter of the impact impule: imum intruion α imum contact force initial velocity υ rebound velocity impact time t and etc. but alo the entire loading proce. υ отскока The indenter gained velocity υ could be changing in the range from 0 to 3 m/. During tet conical indenter were ued with ma of m= g. made from tungten carbide with the tip angle of ϕ =90 and 10 degree. With uch indenter form the crack in the material appear at a lower velocity υ and loading P of intruion a compared to uing of pherical tip. Figure 1 how the character of crack formed in PMMA during intruion of indenter. Developing of crack wa performed in the technical acetone medium. The character length l and quantity n of crack that are formed at intruion coniderably depended on the extent and train rate and alo on the angle of cone opening. Optical meauring that were conducted at tatic indentation howed that formation of the radial crack occurred on the tage of loading with it further growth on the tage of unloading. One of the firt paper in which the fracture toughne wa evaluated wa the Palmqvit work [1]. He howed that calculation hould account for the overall amount of crack and determined dependence between the total length of radial crack l load P applied to the indenter and fracture toughne. n i P l = b1 P b (1) where b 1 and b parameter aociated with the crack reitance and the tate of the urface. i

2 а b c Fig. 1. Crack formed in PMMA during intruion of indenter. a - the tatic indentation with the formation of radial crack b - the tatic indentation with the formation of lateral and radial crack c - under dynamic loading with the formation of radial crack In our calculation a the bae were alo taken the reult of indentation at which it wa poible to oberve formation of Palmqwit radial crack only i.e. in condition when median and lateral crack were abent. For decription of the fracture proce an energetic approach wa ued for calculation of ize for palling fragment at formation of median crack. Let ue thi approach for calculation of the critical tre intenity factor К 1с at formation of Palmqvit radial crack (Fig. ). Fig.. Palmqwit crack. In the [] the following equation for tre intenity factor for crack with length l wa derived: 1 11 πσh = () l Where σ tre acting the crack h - depth of the crack the geometry of which can be decribed by mean of a emiellipe. If everal crack are formed their overall length can be replaced with multiplying of the crack quantity n on their average length l av : 1 11 πσh = (3) nl av Formation of the radial crack occur a a reult of tenile circumferential tre σ θ the exact calculation of which i a difficult problem. It can be accepted equal to the normal σ n if the Harr- Carman condition i met or they can be calculated if it i accepted that the imum circumferential tre appear at the border of the elatoplatic tranition in accordance with approach uggeted in [3 4]. In the econd cae which ha a better theoretical background σ θ i decribed through yield tre σ Т [5]:

3 σ σ Т θ = (4) 3 Taking into conideration the relation between σ Т and material hardne H: We will get: H 3σ Т (5) H σ θ = (6) 9 4P Material hardne a the average contact preure H = for the cone with arbitrary tip angle i π d alo equal to the unit work of diplacement of material volume V: H A 4P = = (7) V πd Where d impreion diameter A work of training that can be derived through the kinetic energy of the falling indenter: mυ A = (8) Taking into conideration that the diplacable volume of the material i approximately equal to the cone volume indented into the material teted on the depth α: πd α V = (9) 1 and alo accepting the fact that the depth of the radial crack (fig. ) a a rule doe not exceed the penetration depth [] h α = d /( tg( ϕ / )) by uing equation (3) (6)-(9) we can obtain: And for tatic indentation: mυ = (10) d nl 1c 0 3 ср P = 1c 0099 d nl tg( ϕ / ) (11) If it i conidered that the purpoe of thi paper wa to invetigate the poibility of applying the method for determination of К 1с and at the ame time a tak wa not et to obtain true value of fracture toughne then accepted aumption concerning the tre value which affect the crack are completely jutified. Beide in [5] wa determined that the tree in the area of contact under the loading a well a after it removal (reidual tree) are proportional for the material hardne. Table 1 how the reult of tatic tet of PMMA with variou indenter at different condition of loading and temperature T. ср

4 Table 1 Р Н Т С 5 ϕ гра 90 КПа М 679±18 65±18 719±19 ϕ гра 10 КПа М 747±19 710±17 7±16 793±1 Т С 0 ϕ гра 90 КПа М 114±18 17± ±1 ϕ гра 10 КПа М 19±19 17±14 11±1 134±11 1c A een from the table the value of do not depend on the loading rate but ignificantly change becaue of the temperature. Increae of fracture toughne i oberved with decreae of temperature. Behavior of the dynamic fracture toughne wa coniderably different (fig. 3). For the range of ' average train rate achieved during meauring ε υ /( α tg( ϕ / )) no clear tendency for = ср change depending on the train rate wa oberved. At the ame time temperature T went down. 1c ha decreaed a the Fig. 3. Dependence of the 1 с = f( ε ) at the teting of PMMA. (1 φ=90 T=-10 C; φ=90 T=5 C; 3 φ=10 T=-10 C; 4 φ=10 T=5 C). Neverthele obtained reult correpond to the common experimental data. In [67] it i hown that train rate and temperature can ignificantly influence the value. Hence the obtained reult 1c

5 how that the given method can be ued at tet of elatoplatic polymer material. The diadvantage of thi method i the difficulty of determining quantity and ize of crack that require application of additional equipment -microcope and penetrant for revealing of crack which alo add ignificant inaccuracy of meaurement. However an undoubted advantage of thi method i the ability to control the real product without manufacture of ample when applying dynamic indentation. Thi method ha become widely ued for control of hardne and device baed on application of impact on the teted material by indenter are widely available. Beide at the appropriate calibration (account of train rate and temperature) it i poible to reduce thee value to thoe obtained by tandard teting cheme. Reference 1. Palmqit S. / Jernkontorent Ann Bd S Niihara. A. / Journal of material cience letter Р Bihop R. F. / Proc. Phy Society Р Marh D. M. / Proc. Phy. Society F 79. Р Johnon. L. / J. Mech and Phy Solid Р Marhall G. P. // Journal of material cience Р Atkin A.G. / Journal of material cience Р