LIFE-TIME PREDICTION FOR POLYMER MATERIALS

Polymer testing including natural, accelerated testing or creep and fatigue testing, etc. is very important to evaluate changes in properties, structure, morphology and durability of polymer materials. This is also the basis for experts to predict the life-time or service working life or safe working life of polymer materials. Thereby, it can contribute to the selection of appropriate technologies and machines to fabricate polymer materials to meet requirements and use in different environments and conditions, especially, in harsh conditions. This review presents an overview of life-time prediction for polymer materials through natural tests or accelerated ageing tests and methods of extrapolating data from induced thermal degradation. The life-time or service working life of a polymer material is the continuous service period of the material from the time it is affected by usage conditions or environment until its decomposition or degradation according to some failure criterion. The accuracy of predicting the life-time of a polymer material depends on a forecasting equation that fully reflects climatic factors, weather, environment, usage conditions, etc. affecting the material as well as the selected failure criterion.


INTRODUCTION
Nowadays, the usage demand for polymer materials is constantly increasing in the fields of engineering, industry, agriculture, healthcare, defense, security and civil use in our country and around the world. The main advantages of these materials are that they are light, more durable than traditional materials, easy to shape at will, easy to decorate, soundproof and good heat insulation, etc. However, during the process of use, due to the influence of natural factors and conditions of use, polymer materials are prone to change in properties, structure, morphology and durability, causing catastrophic failure for users and manufacturers. Over the past thirty years, environmental problems related to the disposal of polymers that have completed their lifecycle have begun to arise, and the need to foresee their end of life has become increasingly urgent. In many cases, polymer materials have been used under severe, long-term or critical application conditions, so a better understanding of the failure mechanism of polymer materials to be able to predict their lifetime. Therefore, the research of characteristics, properties, composition, structure, morphology, durability of polymer materials by various methods such as spectroscopy, molecular weight analysis, elemental analysis, X-ray diffraction, electron microscopy, thermal analysis, mechanical property analysis, electrical property analysis, electrochemical property analysis, environmental resistance, chemical and solvent resistance, etc. is essential to evaluate the ability of their safe use. From there, it is possible to predict quickly the working life of polymer materials for practical applications, particularly while their use in harsh environments.
The most accurate and reliable method of predicting the life-time of polymer materials is by continuous testing in natural environments, in outdoors or under actual conditions of use. This method is widely applied when the life-time of polymer materials is short, for example when they are used under extreme conditions. For rapid prediction of the life-time of polymer materials, the determination of the effectiveness of additives introduced into the polymer by the accelerated test or artificial test is often used. This test simulates the effects of natural conditions or climatic or weather conditions where the material used in combination with acceleration to allow the material to decompose/deteriorate faster without changing the nature of the material degradation mechanism. Some popular life-time prediction methods using accelerated ageing tests are thermal ageing based on Arrhenius model, radiation agein based on power law extrapolation and combined thermal and radiation ageing based on superposition of time dependent data or superposition of dose to equivalent damage (DED) data. This paper presents an overview of the life-time prediction for polymer materials. First, weathering test methods for polymer materials, where testing methods and standard test procedure are considered. Then, we pay attention to degradation of polymers with influencing factors, types and general degradation mechanism of polymers under different conditions. The last section focuses on different methods for predicting the life-time of polymer materials.

Natural exposure
The natural test of polymer materials is to expose them (sheets, films, etc.) to natural contact at outdoor exposure sites or under conditions of use to assess changes in characteristics, properties of polymers, thereby determining the durability, especially the weather stability of polymer materials, and predicting the life-time of polymer materials. The exposure period required should be at least as long as the life-expectance of the product. Standard weathering test procedures for polymers in direct and under glass exposures (ASTM G7, ASTM D1435, ASTM G24), in black box (ASTM D4141, GM 9163P), AIM box (ASTM G201, GM 7455M, GM  9538P, GM 3619M, GM 7454M, GMW 3417, Ford DVM 0020), Q-TRAC Natural Sunlight  Concentrator (ASTM D4141, ASTM G90, ASTM D4364, SA J1961) have been presented in "Q-Lab weathering research service" [1]. Some requirements for natural exposure are as follows: (i) Test site: The test site for polymer materials is the one with climatic/weather characteristics as close to the conditions of use as possible. The ground of the test station and the yard has a short grass layer to regulate the air and reduce the influence of dust, sand and other agents. The natural test site should be located relatively independent from residential areas, industrial zones, and production facilities to limit the effects of highrise buildings, public works, and contaminant factors to the natural test site. This helps to avoid the error of microclimate factors, especially solar radiation, humidity and temperature at the natural test site.
(ii) Test shelves: The test shelf is usually made of metal (stainless steel, aluminum, etc.). The samples are tested in different sizes on the shelf but they can stull stretch naturally during the test process with changing weather factors that can cause evaporation of additives from the surface of the test specimen. The lowest position of the test shelves should be at least 45 cm above the ground so that the specimen not affected during the test. The angle of inclination of the test shelf relative to the ground varies according to the purpose of assessing the change in properties, characteristics, structural morphology and weather stability of polymer materials.
(iii) Sample jig: Polymer samples often have variable dimensions, so when placing the polymer sample on the test shelf, a jig used to fix the test sample on the shelf.
Besides, brackets, shields, test time, etc. are also required in the testing process.

Artificial exposure
Currently, there are different types of accelerated or artificial tests for polymer materials. These tests reflect the influence of one or several climatic and weather factors as well as a combination of the effects of climate and weather factors on the characteristics, properties and morphology of polymer materials. The advantage of artificial weathering is that it is easier to accelerate the testing of polymer materials under standard conditions.

Thermal stability test
The test of thermal stability of polymer materials is a common method used to evaluate the effects of temperature, including the effect of high temperature on the deterioration of mechanical properties, thermal properties, electrical properties as well as changes in structural morphology of polymer materials [3 -9]. From this, the active energy for thermal decomposition of polymer materials can be determined and their life-time can be predicted according to a selected failure criterion, for example, a reduction of 20 % or 50 % in tensile strength or elongation at break from the initial value obtained before testing of polymer materials. In this test, samples are thermally aged at a constant (isothermal) temperature in an inert gas or natural air according to a certain standard, for instance, DIN 53508-00. First, the sample suspended or mounted in a test device was heated to a certain fixed temperature ( The standard procedure for testing thermal stability of polymer materials used the Arrhenius equation according to the ISO 2578. This standard can make long-term prediction from multi-point polymer ageing data only based on the Arrhenius equation or any other procedure. The ASTM D1203 and ISO 176 present effectiveness of plasticizers in polymer materials [2,3].

Artificial light source test
Carbon-arcs, fluorescent tubes, xenon-arcs are the light sources used in an accelerated weathering apparatus, which ideally simulate solar radiation. For artificial testing of polymer material, a fluorescent tube or a xenon-arc lamp test chamber with a wavelength of 315 -420 nm is often used [10 -16]. The test using a solar carbon-arc lamp performed with short wavelength ultraviolet radiation (375 -400 nm) is a rather harsh test. In the xenon-arc lamp test chamber, the xenon-arc lamp continuously generates sunlight radiation (including ultraviolet rays with long wavelengths and visible light as well as very strong radiation at near infrared region wavelengths), which is close to the temperature from midday sunlight. When a radiation filter is used, the intended ultraviolet wavelengths obtained for accelerated testing of polymer films. Currently, carbon-arc lamp testing for polymer materials conforms to ISO 4892: part 5, ASTM D1499-99; xenon-arc lamp testing to ASTM D2565-99 and ISO 4892: part 2 [2]. Standard test procedures for the use of fluorescent tube are in ASTM D4329-99 and ISO 4892: part 3. In addition, some other standards for testing artificial light source for plastics are ASTM G155, ISO 11341, JASO M346, AATCC TM16, TM 169, etc.

Ozone cracking test
The ozone cracking test is very commonly used to evaluate the effect of ozone on the deterioration of mechanical, thermal, electrical properties, and structural morphological changes of polymer and rubber materials, especially unsaturated polymers, natural rubber, and synthetic rubber [15,17]. This test is conducted according to the ASTM D4575-99, ASTM D1171-99, ASTM D1149-99, ISO-1431-1: 2012 (E) standards. Polymer and rubber testing is performed in an ozone chamber with different sample expansion, ozone concentration, and duration of action. The impact of ozone on polymeric and rubber samples is determined according to the crack appearance time, crack size and density on the sample surface.

Salt-accelerated test
Salt-accelerated test is a test that simulates the impact of a salt solution (a corrosive factor) on the deterioration of mechanical, thermal, electrical properties, and structural morphology of polymer materials, especially the deterioration of the surface and protective properties of polymeric paints and coatings, etc. [1,18]. Polymer samples are in spraying with saline solution with different spray time according to ASTM D6675, ASTM D1654, etc.

Fungi and bacteria action test
The effects of fungi and bacteria on polymer materials are determined through visual examination or measurement of changes in mass or physical properties of polymer materials [19].
The general principle of fungal impact testing is to conduct artificial acceleration when placing the test sample (with spray of fungal spores on both sides of the sample and on the nutrient medium) under the most favorable conditions for fungal growth. Spores of the following fungi are commonly used to spray both samples and nutrient media: Aspergillus amstelodami, Aspergillus flavus, Aspergillus niger, Aspergillus versicolor, Chaetomium ND 201, Cladosporium herbarum, Gonytrichum, Paecilommyces varioti, Penicillium waksmani, Penicillium wortmani, Penicillium citrium, Triclderma virede, Scopulariopois brevicaulis, and Curvularia lunata. The standard procedure of fungal impact testing for polymer materials is in the ISO R-846-78.
In addition, accelerated tests that often combine the impact of two or more factors (also known as complex tests) are increasingly used because they contribute to the evaluation of deterioration in properties, durability and structural morphology changes of polymer materials, prediction of their life-time as well as determining the effectiveness of additives introduced into polymer materials. Some typical acceleration tests that reflect the combined effects of two or more factors are UV-thermo-humidity complex test, heat and oxygen impact test, heat and moisture condensation test, UV and salt-accelerated test, etc. [20 -28].

Effect of some factors on degradation of polymer materials
The degradation process of polymer materials is the partial decomposition of polymers into low molecular weight products as well as fragments with large but smaller molecular weights than neat polymers. This is the most common process during the life-time of a polymeric material. Structural changes during degradation process of polymer materials can lead to physical or/and chemical transformations that take place in polymer materials under the influence of degradation factors. These factors are thermal -static heat ageing; sub-zero exposure or thermal cycling; humidity (hot/wet) exposures; weathering (rain, sand erosion, sunlight, etc.); salt water immersion or spray; freeze/thaw and dry/wet cyclic conditions; combined loaded and environmental exposures; ozone, oxygen and chemical substances; UV and light radiation; high energy radiation; electrical stress; and micro-organisms [1, 27].

Degradation types of polymer materials
The degradation of polymer materials is the result of such reactions as chain cutting, scission, crosslinking, thermal oxidation and even destruction. There are two main degradation types of polymer materials, namely chemical degradation and physical/physicochemical degradation. The chemical degradation of polymer materials is caused by oxidation, hydrolysis reactions, etc. while the physical/physicochemical degradation due to heat, shear, UV light, etc. Therefore, the degradation types of polymer materials include thermal degradation (caused by temperature), photo-degradation (caused by light radiation), bio-degradation (caused by organisms), hydrolytic degradation (caused by water), external stimulus degradation (caused by electrical stress), environmental degradation (caused by NO 2 , SO 2 , NH 3 , CO, H 2 O 2 , O 2 , O 3 , metals, etc.) and mechanical degradation (caused by mechanical stress) [1, 27].

General degradation mechanism of polymer materials
Polymer materials can be degraded according to different mechanisms depending on the impact sources, for example, thermal or thermal oxidation degradation, weathering or more specifically photo-oxidation, chemical degradation, environmental stress cracking, ionizing radiation, biological degradation, creep, and fatigue. In general, each type of polymer degradation follows a degradation mechanism, which in turn causes different changes in polymer materials. Thermal ageing and weathering can cause chemical and physical changes while chemical degradation refers to the failure of polymer materials hydrolyzed by chemical attack.
The degradation mechanism of polymer materials begins with an initiation stage, in which free radicals formed by energy from any source such as light, radiation, heat, etc.
Next, propagation occurs through a series of reactions as follows: The final stage is termination, whereby free radicals react with each other:

Definition of life-time of polymer materials
The life-time (or secure working life/shelf life/service life) of a polymer material is the continuous service period of the polymer material starting from when the polymer material is affected by conditions/environment of use until it is decomposed or deteriorated according to a certain failure criterion.
The life-time of polymer materials is closely related to their weather durability. It is a stable working time in natural environments, outdoors (with the impact of climatic factors and weather) or accelerated conditions that simulate the effects of climatic factors and weather, without obvious deterioration in properties, durability and morphology of polymer materials.

Scientific basis for predicting life-time of polymer materials
The scientific basis for predicting the life-time of polymer materials is that failure, degradation or deterioration of the properties, characteristics, durability, and structural morphology of polymers must fully reflect climatic factors, weather, environment, conditions of use, etc. affecting polymer materials. In addition, the failure criteria, the deterioration of characteristics and properties of the selected sample may or may not be the most typical. The accuracy of the polymer materials' life-time prediction depends on the test method, the nature and origin of the polymers. During the impact of climatic factors and weather on polymers for a certain period of time, one or more characteristics or properties of the polymer materials are deteriorated, leading to a decrease in durability, usability, recycling ability and reprocessing ability of polymers.
In fact, some degradation processes of polymer materials occur in a very short time, while others can take decades to reach equilibrium, meaning that the decline does not happen anymore. During the test process, there is a continuous decline in the properties of the polymer material, showing a tendency decreasing to a certain value called the dynamic equilibrium state. In practice, for most materials, there are both types of above declines with various degrees. In addition, the terms such as long-term decrease (irreversible) and temporary decrease (reversible) are used. A polymeric material considered to suffer long-term degradation (irreversible) when it has undergone prolonged deterioration caused by the effects of climatic and weathering factors, bringing the degradation to a critical level. In the meantime, a polymer is considered to have degraded temporarily (reversible) when the degradation disappears as soon as the climatic factors/weather drop below the critical threshold or stops due to the impact of one or more climatic factors/weather or some other reasons. For temporary decrease process, the test can be performed under simulated laboratory conditions without acceleration, while for long-term deterioration, the material should be tested under accelerated conditions to obtain laboratory results more quickly.
During natural testing, the polymer materials will exhibit similar weather resistance in regions with the same climatic conditions. Thus, it is possible to set up typical climate test stations in regions with the most reference typical climate, in which the properties and durability of polymer materials, especially the weather resistance, are determined. Their life-time can also be predicted in other similar climates around the world according to the failure standards for polymer materials.
In general, degradation and ageing of polymer materials alter their mechanical-, physical-, thermal-, and electrical properties, leading to a reduction in their usability, shelf life, etc. In particular, changes in mechanical properties of polymers (elongation at break, tensile strength, impact strength, flexural strength, elastic modulus, flexible modulus, etc.) are often quite sensitive due to the effect of one or several factors causing polymer degradation [27,29]. Some popular models exhibiting a correlation that reflects the deterioration in mechanical properties of polymer materials over time in either natural or artificial tests are as follows: -Linear: y = a + bx (4.1) -Parabolic: y = a + bx + cx 2 (4.2) -Exponential: The most appropriate model is the one with the reliability coefficient or linear regression coefficient r 2 (calculated by a computer-based statistical analysis system) which can be achieved as high as 1 [28].
Until now, the Arrhenius equation is still considered and used for establishing the equation that predicts the life-time of polymer materials: (4.5) where, : life-time, year; E α : activation energy of polymer degradation reaction, kJ/mol; T: test temperature, o K; R: ideal gas constant (8.314 J/mol o K); A: the exponential pre-factor, characterizing the probability of a polymer degradation reaction.
Transforming Eq. 4.5 to a logarithmic form: where, A and E α can be determined by using: (i) experimental data; (ii) the least squares method; (iii) differential methods; (iv) multiple heating rate calculation methods.
A plot of log or ln against 1/T should yield a straight line with a slope of E α /R, which can be extrapolated with the caution.
In general, the Arrhenius equation is the first choice to evaluate the influence of temperature on a property of polymer materials but no general rule can be given for the measurement of reaction rate to be used. A failure criterion indicates the remaining percentage of this property from its initial value and is chosen to assess the life-time of polymer materials.
When a form of the change in parameter with testing time is proposed, the power law is often applied first: ( ) (4.8) Combining Eq. 4.8 with Avrami equation 4.9 gives Eq. 4.10: where K 0 is the reaction rate at a reference temperature T 0 , K the reaction rate of the process, T absolute temperature, A and B are constants, n is the reaction order, t testing time, E the reaction energy, and R is the gas constant.
When the properties of polymer materials are changed with time in the degradation process, the rate of the change of those properties with the level of one or more degrading agents can be recorginzed. A series of semi-empirical relationships (linear and logarithmic) for the degradation of polymeric properties have been proposed. They usually take the form: where k is the reaction rate or degradation rate, P the polymeric property, T the ageing temperature (in K), t the ageing time, and n an experimentally determined constant.
The strength of polymer materials decreases exponentially with testing time to an asymptotic value (usually zero). The limitation of this approach lies in the assumption that only one time-dependent process is occurring, although in practice, several processes can occur simultaneously. Therefore, an extended approach to determine the combined effect of temperature, stress and moisture with the failure time t f is given: where T is absolute temperature, C and b constants, E α the activation energy, R gas constant, and S the uniaxial stress.
Changes in the properties of polymer materials under the impact of ionising radiation can be predicted using a time-temperature-dose rate superposition principle. The model is based on the Arrhenius expression and the dependence of degradation vs time obtained at different temperatures can be given by a shift factor a T : where T 0 and T represent the reference and service temperatures.
Converting Eq. 4.13 to logarithmic form: ( ) (4.14) Equation ( where, a T0 and a Te are the shift factor for the reference temperature and the extrapolated shift factor for operating temperature, respectively; t 0 is the life-time of the polymer material at the reference temperature. The Williams-Landel-Ferry (WLF) model is also applied to predict the life-time of polymer materials based on any physical property through the temperature induced physical/chemical changes as a function of processing and storage conditions. This model uses a TTSP without any additional assumptions regarding the dependence of the properties of polymer materials on time at any temperature: where C 1 and C 2 represent the experimental constants, which depend on temperature and the nature of the material and can be calculated as follows:  where,  is the heating rate and T p is the temperature peak.
Sbirrazzuoli equation: where, x = E α /RT is the minimized activation energy at temperature T. E α in this equation is assumed to be constant. Kissinger-Akahira-Sunose equation:  [4]. In this study, the Arrhenius equation was used to predict the life-time of the nanocomposites. The authors indicated that the life-time of HNBR at 40 o C was improved up to 45 years in the presence of 8 wt.% of organo-modified clay as compared to the HNBR life-time of 15 years. This is explained by the presence of the organo-modified clay, which has high thermal stability and is regularly dispersed in the HNBR matrix at nanometer size, and thus acts as a barrier to prevent the penetration of oxygen and heat into the HNBR matrix, resulting in reduced oxidative decomposition and rupture reactions of HNBR.
In another report, the life-time of polyvinylchloride (PVC) was forecasted by thermal ageing methods at different temperatures (105 o C, 120 o C and 135 o C) based on a reduction of 50 % in elongation at break of PVC samples [7]. Two PVC samples chosen for investigation were the PVC-I containing thermal stabilizers such as cadmium stearate, barium stearate, 2,4-toluylene diisocianate trimer; a plasticizer -dioctylphthalate; an antioxidant -bisphenol A; and the PVC-II containing thermal stabilizers such as cadmium stearate, barium stearate, dilauryl dilaurate tin, and a plasticizer -dioctylphthalate. Table 4.1 presents the time for decreasing 50 % of elongation at break of the two PVC samples after thermal ageing.  Hamid et al. reported that the correlation coefficient between a natural test in Africa Saudi and an artificial test in an Atlas Ci65 weathering test instrument (ASTM D 2565) was 2.8 times (5,000 hours of artificial test corresponding to 14,000 hours of natural test) [28].
The results from a natural test in Dong Hoi (Quang Binh, Viet Nam) showed that the half-life time of high density polyethylene (HDPE)/organo-modified CaCO 3 composite sheet was 25.6 months [31]. The correlation coefficient between the natural test in Dong Hoi and an artificial test in a UV-CON 327 weathering test instrument using each cycle of 8 hours of UV irradiation at

Methods for predicting life-time of polymer materials based on deterioration of thermal properties
The life-time of polymer materials can be predicted by thermal analysis methods based on the deterioration of properties combined with changes in weight or heat of the sample. Thermal gravimetric analysis (TGA) is a useful technique to calculate the kinetic parameters of the degradation process of polymer materials.  where, C ox is the constant corresponding to A in Eq. 4.26.
The failure time of linear low density polyethylene (LLDPE) samples modified with chemical agent (grafting), physical agent (Al(OH) 3 ) and unmodified was predicted owing to the graph depicting the dependence of ln t f(OIT) on 1/T, where the OIT was determined at different temperature ranges (190 -220 o C, 180 -210 o C and 210 -240 o C). Table 4.3 indicates the E α of thermo-oxidation process, correlation coefficient (r 2 ) and failure time of LLDPE samples, which increases from chemical modified LLDPE, up to unmodified LLDPE, then up to physical modified LLDPE [40].

Methods for predicting life-time of polymer materials based on deterioration of chemical and physical properties
Changes in physical and chemical properties during testing can be used to predict the lifetime of polymer materials. Malic et al. based on the loss of HALS in LDPE and PP films to predict the photo -stabilization time of these films [3]. The failure criterion applied to evaluate the photostabilization time of these films was an increase in the absorption intensity of the carbonyl group in the infrared region by up to 0.3 (T-03). The authors determined that the photo -stabilization time or protect time (T-03) of PP and LDPE was 30-40 hours and 270-310 hours, respectively. Besides, owing to Billingham and Calvert's theoretical model of stabilizer weight loss, the authors also found that the photo -stabilization time at a HALS weight loss of 0.2 (80 % reduction in HALS weight) for LDPE/HALS and PP/HALS films was 2,530 hours and 1,130 hours, respectively.

Methods for predicting life-time of polymer materials based on deterioration of fatigue and creep properties
In recent years, polymer materials with high modulus and durability have been developed to meet the demand for advanced lightweight materials and applied load (static and fatigue) materials working in hostile environments. Therefore, it is necessary to develop test procedures to evaluate the shelf life/working life of these materials in hostile environments. Since the lifetime of polymer materials is usually measured in years, it needs to be predicted through accelerated testing. The effect of long-term loads on the deformation and failure behavior of polymer materials is important for predicting their failure time.
Creep behavior is the increase in strain or deformation of a material at the time when the material tested at a constant load over an extended testing period. The dependence of creep inside polymer material on the testing time is as follows: In the first stage, primary creep starts at a rapid rate and slows down over time; creep in the second stage occurs at a relatively uniform rate; and in the third stage, creep takes place at an accelerated rate and terminates due to material failure at the time of rupture [3].
Fatigue is often expressed in terms of maximum applied fatigue stress S and fatigue life (number of cycles to failure N f ). This property is suitable to predict the fatigue performance of composite laminates (including statistical, fracture mechanics, empirical models) [3]. where SDR m and SDR f are the strength degeneration ratios of matrix and fiber, respectively, f m is the weight ratio of matrix in the composite, Δlnf is ageing effect caused by the fiber/matrix interface in the composite.
The model used to predict the life-time of the composites is as follows: (4.29) The TTSP is an effectivel tool to predict the life-time of polyurethane (PU) derived from glycol ester (poly(ethylene adipate) glycol), 4,4 -dibenzyldiisocyanate and the extension partsdiethylene glycol (DEG) and trimethylol propane (TMP). The PU composites containing different TMP contents changed from 0 to 1.8 %, 2.6 % and 3.4 % in weight were assigned as PU-DEG, PU-DEG-1.8 TMP, PU-DEG-2.6 TMP and PU-DEG-3.4 TMP, respectively [47].
Based on the modulus curves, the authors calculated the shift factor and activation energy of the PU composites using Williams-Landell-Ferry (WLF) model. Some parameters based on the DMA behavior of PU composites indicate in Table 4.4 [47].
Paul et al. evaluated the failure time of nylon-6 using TTSP and dynamic mechanical analysis (DMA) technique based on the test data according to ASTM D2990. The authors predicted the failure time of nylon-6 to be about 6 weeks [48].
Rui Miranda Guedes assumed that the unidirectional strain response of a linear viscoelastic material, under arbitrarily stress,  t can be expressed by the power law [49]: where D 0 , D 1 , n are material constants,  0 is time unity. The prediction of failure time of a material with viscoelastic properties under fatigue (creep) testing when a load  0 applied under instantaneous condition with loading  R is calculated according to the following criterions: Reiner-Weissenberg (R-W) criterion: Maximum Work Stress (MWS) criterion: Maximum Strain (MS) criterion: where F a =  0 / R (4.34) is normalized applied stress.
Based on the creep properties of glass-fiber/urethane composites as well as the TTSP and R-W, MWS, MS criteria, the authors found that the experimental data are complied with the R-W and MS failure criteria.
Bora et al. gave a model for predicting the life-time based on the impact-fatigue properties of carbon fiber reinforced poly (ether imide) composites [50]. The parameters such as the impact number until fracture and the impact energy used to establish the impact-fatigue life curve expressed as follows: y = 1.2226.10 12 [e (x/-0.02737) ] + 90.66097 (4.35) where y is impact energy and x is impact number.
The "strain-life time" method has been used to predict the life-time of carbon fiber reinforced poly (lactide-co-glycolide) composites [51], which can work under the same usage conditions as in a simulated human body environment below 1,000 cycles of loading. Nguyen Thien Vuong determined the correlation coefficient between the accelerated test (samples were exposed in a UVCON UC-327-2 weathering test instrument according to ASTM D 4587-91) and the natural test (samples were exposed to the open air in Ha Long (Quang Ninh, Viet Nam)) to be 1.33, based on the change in surface gloss property of acrylic coatings [53]. The activation energies, E α , of polycarbonate, poly(ethylene terephthalate) and resorcinol polyacrylate obtained from the bending test data after a hydrolysis process at a temperature of 65-95 o C and a relative humidity of 23-95 % were 92 kJ/mol, 129 kJ/mol and 102 kJ/mol, respectively [55].  Bellenger et al. also determined the activation energy (E α ) of hydrolysis process of poly(3hydroxybutyrate-co-3-hydroxyvalerate) (PHBV) based on the adsorption rates of different types of water. It was found that the E α was 70 kJ/mol, 43.7 kJ/mol and 56.5 kJ/mol for salt water, deionized water and distilled water, respectively [57].

Some other methods for predicting life-time of polymer materials
From the data of total UV radiation (TUVR) energy combined with the natural test, the lifetime of homopolypropylene, polypropylene random-copolymer, and polypropylene impactcopolymer were predicted to be about 1,160 hours, 796 hours and 755 hours, respectively [10]. where a, b are the parameters depending on stablility of materials and temperature; λ 1 and λ 2 are the limited wavelength of radiation causing the polymer oxidation; I a is the intensity of light absorbed at wavelength λ; E α is activation energy; T is absolute temperature.
Meng Huang and Yuanxiang Zhou set up the space charge dynamics based model to predict the life-time of insulating polymers, for example, LDPE [59] as follows: where, L h is the life-time of material, N the trap density, K T the trapping coefficient (K T = 8.66.10 −5 s -1 ), K D the detrapping coefficient (K D = 1.32.10 −5 s -1 ), p c the critical released energy density rate, and U p the electromechanical energy.
In addition, the life-time of polymer materials can be evaluated based on Lambert W function: where, L l is the life-time of material, w c is the cumulated released energy density.
When comparing the calculated lifetime of static and dynamic breakdowns (Eq. 4.40 and Eq. 4.43) with the experimental data, the authors indicated that the life-time of LDPE decreased with increasing electric field, and the difference between the static and dynamic breakdown models was very small and the life-time prediction obtained from these models was in good agreement with the experimental data.
From the data on plasticizer content, volume mass, water adsorption coefficient and water vapor permeability of poly(vinylchloride) (PVC) after natural testing, the life-time of PVC was predicted to be about 30 years [59].
Ariannik et al. based on the degree of polymerization (DP) of cellulose to predict its lifetime [60]. When DP of cellulose reached 200, the estimated life-time of cellulose in case I (load limit of 75 %) and case II (load limit of 100 %) was 80.4 years and 42.5 years, respectively.

CONCLUDING REMARKS
In order to predict the life-time or service working life of polymer materials, there are some methods to test and evaluate the change in characteristics, properties, morphology, durability, etc. of these materials. Common weathering tests for polymer materials are natural exposure test and artificial exposure test, in which the latter includes thermal ageing test, light source test, ozone cracking test, salt-accelerated test, fungal and bacterial activity test.
The degradation mechanism of polymer materials is very complicated due to the profound influence of one or more factors such as chemical factors, physical factors, mechanical factors, biological factors, weather, and climate, etc.
From the degradation data of polymer materials, it is possible to predict the life-time of polymer materials when applying the Arrhenius equation and power law model. However, these models are not applicable to all cases of degradation data of polymer materials. Therefore, a time-temperature superposition principle is used to improve the accuracy of predicting the lifetime of polymer materials and the activation energy of the degradation process. Williams-Landel-Ferry and Friedman methods are also used to predict the life-time of polymer materials in the case of temperature-independent changes of properties or diffusion-limited degradation processes.
The iso-conversional methods are reliable kinetic methods for processing thermal analytical data obtained after testing polymer materials. They allow the activation energy to be determined without assuming any specific form of the reaction model. The activation energy is mainly used to predict the life-time of polymer materials in the case of physical and chemical processes occurring within the material.
Scientists are still developing new methods or improving existing ones to predict the lifetime of polymer materials due to their great interests and various applications in almost all areas of engineering and our life.