Indentation size and loading rate sensitivities on mechanical properties and creep behavior of solid bitumen

International Journal of Coal Geology 216 (2019) 103295

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International Journal of Coal Geology journal homepage: www.elsevier.com/locate/coal

Indentation size and loading rate sensitivities on mechanical properties and creep behavior of solid bitumen

T

⁎

Yuke Liua,b, Yongqiang Xiongb, , Kouqi Liuc, Chao Yangb, Pingan Pengb a

Guangzhou Marine Geological Survey, China Geological Survey, Guangzhou 510075, China State Key Laboratory of Organic Geochemistry, Guangzhou Institute of Geochemistry, Chinese Academy of Sciences, Guangzhou 510640, China c Department of Petroleum Engineering, University of North Dakota, Grand Forks, ND 58203, USA b

A R T I C LE I N FO

A B S T R A C T

Keywords: Solid bitumen Nanoindentation Creep Mechanical properties

Creep behavior of rocks could impair fracture conductivity and wellbore stability during gas production from highly matured organic-rich shales in South China, of which the organic matter is mainly in the form as solid bitumen and is thought to be a major contributor for the creep deformation. To get a better insight into this phenomenon, this paper for the first time characterizes the mechanical properties and creep behavior of a millimeter-sized solid bitumen sample by using quasi-static state creep tests and Dynamic Mechanical Analysis in nanoindentation, and reports their dependences on indentation size and loading rate, respectively. Mechanical properties (including hardness and Young's modulus) are found to be negatively related with both indentation size and loading rate. The extremely small creep strain rate sensitivity (m) of solid bitumen indicates a localized shear flow inside. And m exhibits slightly positive dependences on indentation size and loading rate. The potential mechanisms controlling the deformation of solid bitumen under indentation are also discussed.

1. Introduction Great achievement of shale gas evaluation and exploration have been made in the lower Paleozoic marine shales of the Upper Yangtze region, South China (Zou et al., 2010; Tan et al., 2014). Marine organicrich shales in South China are characterized with extreme low porosity and low permeability, which requires drilling and hydraulic fracturing for hydrocarbon production. In petroleum engineering, consideration of underground dynamics is prerequisite when applying hydraulic fracturing, of which creep deformation of rocks is an important factor. Creep refers to the time-dependent deformation of the materials under a long-lasting constant stress (still below yield strength), which is a behavioral result of rheological properties. Due to the creep behavior of rocks, the dropping of fracture conductivity could result in inaccurate prediction and inefficient production of shale gas (Patzek et al., 2013); and the subsequent reservoir subsidence could impair wellbore stability during gas exploration (Schoenball et al., 2014). However, the intrinsically heterogeneous microtexture in organic rich shales indicates that the macroscale physical performance of shale depends on its microstructural mechanical properties. Such multiscale complexity requires a complete understanding of the role played by each constituent (i.e. organic and inorganic components) in the plasticviscoelastic properties at a finer scale. Previous studies point out the ⁎

significant creep deformation of organic-rich shales is mainly due to the porous clay/organic composite phase (Sone and Zoback, 2014; Rassouli and Zoback, 2018), and the in-situ organic matter is not perfectly a solid material, which flows under high stress (Mighani et al., 2015). Marine shales in South China are at gas window with extremely high thermal maturity (vitrinite reflectance, Ro = 2.0%–3.5%) (Xiao et al., 2015), of which an abundance of organic matter presented as solid bitumen due to thermal cracking of crude oil (Tian et al., 2015; Tuo et al., 2016). As a major component of organic matter, the mechanical and rheological properties of solid bitumen would partially affect the geo-performance of highly mature shales in South China. In this view, quantifying the basic mechanical properties and creep behavior of solid bitumen is fundamental for understanding the elasticity and rheology of organic-rich shale at macroscale, as the latter one is quite essential for compiling rock models simulating underground dynamics, which could optimize hydraulic fracturing design and estimate hydrocarbon reservoir performance during the shale gas exploration in South China (Chen et al., 2015; Sharma et al., 2019). So far, mechanical and creep experiments of geological samples have mostly been performed by using conventional compression test on inch-sized samples at the macroscale (Li and Ghassemi, 2012; Sone and Zoback, 2014), whereas core plugs are not always retrievable. The advanced in-situ mechanical testing method, nanoindenter, has been

Corresponding author. E-mail address: [email protected] (Y. Xiong).

https://doi.org/10.1016/j.coal.2019.103295 Received 19 April 2019; Received in revised form 16 September 2019; Accepted 17 September 2019 Available online 23 October 2019 0166-5162/ © 2019 Elsevier B.V. All rights reserved.

International Journal of Coal Geology 216 (2019) 103295

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proven to be a powerful technique to probe directly into the physical properties of targeted phase at extremely small scale (Goodall and Clyne, 2006; Janakiraman and Aldinger, 2010; Hackney et al., 2013; Wu et al., 2016a,b; Wen et al., 2017; Herbert et al., 2018; Liu et al., 2018c; Xu et al., 2018). This novel technique is capable of measuring both mechanical and rheological properties of materials, with advantages including small volume requisition of samples (like metrics) and rapid data acquisition. Nanoindenter characterizes the creep behavior of the materials by monitoring the changes of indentation depth beneath the indenter with a constant load over a period of time. Another function, Dynamic mechanical analysis (DMA), has been widely used to analyze the viscoelastic-plastic properties of metals, polymers, concrete and shales (Herbert et al., 2008; Wilkinson et al., 2015; Liu et al., 2018b). Simplified as applying an oscillating force to a sample and monitoring the corresponding displacement, this mode can also be used to analyze the Indentation size effect (ISE, introduced later) of mechanical prosperities by monitoring the changes of stiffness, hardness and Young's modulus continuously during loading period. Indentation size effect is a phenomenon that mechanical behaviors, including hardness and elastic modulus, and creep properties of the material, change with indentation depth, which should be considered during indentation tests. Previous studies of the creep behavior of metals (Nix and Gao, 1998; Cao et al., 2009a; Cao et al., 2009b; Shen et al., 2012; Wen et al., 2017; Zhao et al., 2018) indicate that both hardness and creep behavior show a remarkable ISE, that is the hardness and creep strain rate sensitivity being smaller at deeper indentation displacement (Nix and Gao, 1998; Cao et al., 2009a,b; Shen et al., 2012; Wen et al., 2017; Zhao et al., 2018; Li et al., 2019). In addition to experimental results, atomistic simulation with analytical models has been applied to interpret ISE on hardness (Nix and Gao, 1998; Huang et al., 2016). However, some metallic films exhibit a reverse ISE, that is the creep strain rate sensitivity increasing rapidly with enhanced peak load (Cao et al., 2009b). Apart from ISE, mechanical properties and creep behaviors of materials have also been found to exhibit strong dependence on indentation loading rate, as typically a higher loading rate resulting in a larger hardness and a smaller creep strain rate sensitivity (Elmustafa and Stone, 2002; Li and Ngan, 2004; Zhao et al., 2018). However, a reverse loading rate sensitivity for hardness has been reported with some nanocrystalline metals (Karimpoor et al., 2003; Picu, 2004; Wang et al., 2006) and conventional alloys (Fan et al., 2006), namely the hardness value decreases with increasing indentation loading rates. So far, research about ISE and loading rate sensitivities of hardness and creep behavior of geological samples has seldomly been conducted. In spite of extensive research about mechanical property of in-situ and isolated organic matter (Liu et al., 2018a,b,c; Veytskin et al. 2017; Mashhadian et al. 2018), the rheological property especially the creep behavior, and its dependence on ISE and loading rate, have seldomly been investigated, which is partially due to the unavailability of inchsized organic matter samples from field for conventional compression test. Comparatively, based on extremely small volume of samples, nanoindentation test could provide even more information about creep deformation and mechanism of materials at fine scale. This project for the first time investigates the mechanical properties and creep behavior of a small solid bitumen (millimeter scale) with the application of nanoindenter. Three objects are aimed to be finished: characterizing the influences of indentation depth and loading rate on 1) mechanical properties and 2) creep behavior of solid bitumen; and 3) discussing the potential deformation mechanisms. Based on small sample size and time scale, this study could provide us with a general background for the creep deformation of pure organic matter, which is very indicative for further characterization on the creep behavior of bulk organic-rich shales.

Fig. 1. Solid bitumen embedded in epoxy and mechanically polished.

2. Experiments 2.1. Sample and preparation The solid bitumen sample was collected from Shuiquan Formation, eastern Tarim Basin, China, which has a TOC of around 98%. Sample was embedded in epoxy resin and then prepared for laboratory testing by mechanical polishing. Silicon carbide sand paper with sizes from 1200 to 2000 grit was firstly used to polish the sample surface. With aluminum oxide suspension polishing fluid (grain sizes of 2 μm and 0.25 μm), a polishing machine was furtherly used for 30 min to guarantee a smooth surface. Fig. 1 shows the sample after preparation procedure. According to the tomographic image obtained by Dimension 3100 (Bruker Nano/Veeco, Inc., CA) AFM with Nanoscope V controller and Nanoscope 7.3 software, the root mean square (RMS) for an area of 10 × 10 μm2 is 3.43 nm (Fig. 2). 2.2. Experiments 2.2.1. Raman spectrum HORIBA-JY Xplora delicate-type multi-functional fully automatic micro-laser Raman spectroscope with the solid laser device 532 nm/ 30–50 mW was used. 2.2.2. X-ray diffraction The X-ray diffraction (XRD) spectrum of this solid bitumen was generated on a Rigaku XRD Advanced D/max-2200× diffractometer equipped with a Cu tube (Cu Kα radiation of wavelength 1.540598 Ȧ ) operating at 40 kV and 20 mA, and a monochromator. Scan range (2θ) was from 10 to 80°, at intervals of 0.02. 2.2.3. Nanoindenter A diamond Berkovich indenter (Anton Paar NHT3 Nanoindenter) was chosen for this study. Stiffness threshold was 500 N/m and the spring compliance was 0.571 mm/N. Before actual measurements, the tip shape imperfection was calibrated by indenting into a fused silica standard specimen. For all indentation tests, the indenter was set to approach and retract the surface of the sample at a rate of 2000 nm/min within a vertical distance of 2000 nm from sample surface. 2.2.3.1. Dynamic mechanical analysis 2.2.3.1.1. General background. In DMA method, an oscillatory component is applied to a quasi-static loading profile, which could result in a phase shift lag (δ) between strain and force oscillation (Sepe, 1998). This type of test can provide the viscoelastic properties of material by calculating storage modulus (E') and loss modulus (E"). The 2

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Fig. 2. 3D topographic image of solid bitumen from atomic force microscopy (area 10 × 10 μm 2, RMS = 3.43 nm).

constant rate; tertiary (or accelerating) stage with an abruptly increasing rate leading to final failure (Scholz, 1968). However, depending on the active mechanisms and kinetics, which vary for different rock types, test conditions and durations, all three regimes may not be observed in a given test (Goodall and Clyne, 2006). Quasistatic creep test by nanoindenter is based on the assumption that the observed sample deformation is solely steady-state creep deformation, and the creep rate variation over time belongs to stationary creep stage (Mighani et al., 2015). 2.2.3.2.2. Determination of the creep strain rate sensitivity (m). Creep strain rate sensitivity, m, is a power law exponent without unites to reflect the flow ability for a material, which could imply the deformation mechanism. The creep strain rate sensitivity of solid bitumen was determined by using the curve of indentation time and depth during holding period, which is supposed to be a steady-state loading process. A power law relationship (Bower et al., 1993) is generally adopted to depict the steady-state creep behavior:

storage modulus and loss modulus represent the elastic portion or stored energy and viscous portion or dissipated energy of the material, respectively. They are defined by the following equations:

E′ =

σ0 cos δ ε0

(1)

E′ ′ =

σ0 sin δ ε0

(2)

where σ0 and ε0 are stress and strain, respectively, and δ is the phase shift lag between stress and strain (Herbert et al., 2008). The material is purely elastic when phase shift is 0°, and purely plastic when the phase shift is 90°. A phase shift between 0° and 90° indicates the viscoelastic property of material. δ is often used in form of tanδ as:

tan δ =

E′ ′ E′

(3)

The higher the value of tanδ is, the more plastic deformation happened to the material. The indentation storage and indentation loss moduli (E' and E") are given by:

E′ π ⎛ F0 = cos δ + mω2 − Ki⎞ 1 − ϑ2 2β Ap ⎝ h 0 ⎠ ⎜

Q ⎞ ε ̇ = Aσ n exp ⎛− ⎝ RT ⎠

where ε ̇ is the creep strain rate, A is a constant, σ is the applied stress, Q is the activation energy, R is the universal gas constant, T is the temperature and n is the power law (creep) exponent (which equals to 1/m, m is the creep strain rate sensitivity). In this study, as all the nanoindentation creep tests were conducted at room temperature, the temperature was considered to be constant, therefore the Eq. (6) could be simplified as:

⎟

(4)

′

E′ π ⎛ F0 = sin δ − Di⎞ 1 − ϑ2 2β Ap ⎝ ωh 0 ⎠ ⎜

(6)

⎟

(5)

where ϑ is Poisson's ratio, β is geometrical term, Ap is projected contact area, F0 and h0 are force and displacement amplitudes, and δ is phase shift between force and displacement. Ki and Di are stiffness and damping coefficient of the instrument respectively. ω = 2πf, where f is the frequency and m is the mass of the indenter. All the oscillation parameters of the instrument (including stiffness, indenter mass, etc.) are determined during dynamic calibration procedure. 2.2.3.1.2. Parameter setting. In this study, the DMA model was used during loading period, which can provide the variation of mechanical properties, including hardness and Young's modulus, with increasing depth. The loading was conducted at a constant strain rate of 0.05 s−1 with a frequency of 10 Hz and a load amplitude of 5 mN. When the maximum load 50 mN was reached, the load was held for a period of 10 s and being unloaded at a rate of 100 mN/min.

ε ̇ = C1 σ n

(7)

Q ⎞ C1 = A∙exp ⎛− ⎝ RT ⎠

(8)

Considering the geometrical similarity of the Berkovich indenter, the strain rate and the stress can be calculated as:

ε̇ =

1 dh h dt

(9)

P σ= 24.56h2

(10)

where h is the indentation depth, t is the indentation time, P is indentation force. Eq. (7) can be rewritten as:

2.2.3.2. Quasi-static creep test 2.2.3.2.1. General background. The quasi-static creep test involves applying a loading force into the sample surface, and being unloaded after a holding time. During the holding time, the applied force remains constant, whereas the displacement is recorded to increase as a result of creep behavior (Liu et al., 2018b). Based on the relationship between creep strain rate and time from macroscale creep test, the creep has been described as consisting of three stages: transient (or decelerating) stage with a decreasing rate; secondary (or stationary) stage with a

n 1 dh P ⎞ = C1 ⎛ 2 h dt ⎝ 24.56h ⎠

(11)

Taking the logarithm on both sides of the Eq. (11), the creep strain rate sensitivity m can be calculated as:

m=

3

( ( )) ( ( ))

d log d (logσ ) 1 = = n d (log ε )̇ d log

P 24.5h2 1 dh h dt

(12)

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2.2.3.2.3. Programmable procedure. The nanoindenter creep tests were performed on the surface of solid bitumen by using a combination programmable procedure of the constant strain rate method and the constant load method (Lucas and Oliver, 1999). With the purpose of evaluating the experimental repeatability and obtaining statistical results, 10 tests were performed for each parameter combination. The tests to understand the influence of the indentation size effect on creep behavior includes three stages: (1) Different values of the maximum depth (hmax = 1, 1.25, 1.5, 1.75, 2, 3 and 4 μm) were conducted at a constant strain rate of 0.05 s−1; (2) When the hmax set was reached, the maximum load was kept and held for a period of 100 s; (3) Then the indenter was unloaded at a rate of 100 mN/min. Fig. 4. Typical XRD spectrum of solid bitumen.

Similarly, three steps are used to study the effect of the loading strain rate on creep behavior:

2011). According to Bragg's Law, that is λ = 2dsinϑ (λ = 1.5406Ȧ ), solid bitumen has a lattice constant of ~3.40 Ȧ , which is a little larger than the one for graphite (3.34 Ȧ ). The XRD spectrum indicates that solid bitumen is mainly consisted of aromatic carbons, while still containing amorphous aliphatic carbons. The structure of solid bitumen is not as highly ordered as graphite.

(1) Different strain rates (0.005, 0.01, 0.03, 0.07 and 0.1 s−1) were performed with a hmax of 3 μm; (2) When the hmax 3 μm was reached, the maximum load was kept and held for a period of 1200s for each rate; (3) The indenter was unloaded at a rate of 100 mN/min. The maximum displacement set (4 μm) in this study is far < 10% of the sample thickness (~2 mm), thus the substrate effect could be eliminated (Saha and Nix, 2002).

3.2. Dynamic mechanical analysis 3.2.1. Load-displacement and load-time curves A schematic loading profile of DMA mode on solid bitumen is shown in Fig. 5. The load-displacement (Fig. 5a), load-time and displacementtime (Fig. 5b) curves during loading period are zoomed in to show the oscillation details. The hardness and Young's modulus are calculated to be 1.43 GPa and 7.11 GPa, respectively (Oliver and Pharr, 1992). Noticeably, the unloading curve does not completely retrace the loading one but still returns to the original point. Such hysteresis loop is commonly observed with graphitic materials, and the area between loading and unloading curves represents the energy dissipated by the interplanar slip with friction (Field and Swain, 1996; Iwashita et al., 2002; Ozcan et al., 2009). Richter et al. (2000) suggests that the interlayer carbon atomic forces in graphite are so weak, thereby during the unloading period, the interface is extracted at a speed which is faster than the relaxation speed in the lattice. As the ratio of residual indentation depth to maximum depth is far < 0.7, no work-hardening occurred throughout the tests, and the model suggested by Oliver and Pharr (1992) based on elastic contact works well on solid bitumen.

3. Results 3.1. Raman and XRD spectra Fig. 3 shows a typical Raman spectrum, which is used to obtain the maturity of solid bitumen. According to the formula: Ro % = 1.1659 × h(Dh/Gh) + 2.7588, where h(Dh/Gh) refers to Raman peak height ratio, Dh refers to peak D (shift at ca. 1250–1450 cm−1) height and Gh refers to peak G (1500–1605 cm−1) height (Liu et al., 2012), the Raman reflectance is calculated to be 3.68 ± 0.02% with 10 tests on different areas. A representative XRD spectrum of solid bitumen is displayed in Fig. 4, which mainly shows two broad humps arising from the carbon structure. Being analogy with graphite, the highest (002) peak at 2θ = ~26° is attributable to the stacks of aromatic molecules (Koch and Christiansen, 1993), which has a shoulder (100) bump at 2θ = 43°, indicating the existence of in-plane structure of aromatics. The γ-peak at about 2θ = 19° represents the aliphatic carbon structure (Tong et al.,

3.2.2. Relationship between mechanical parameters and displacement The corresponding changes of the Young's modulus and hardness (Fig. 6a), storage and loss modulus (Fig. 6b), and strain lag tanδ (Fig. 6c) with increasing loading displacement are obtained simultaneously. Mechanical properties are significantly affected by ISE during the first ~1000 nm, as hardness and modulus exhibit falling trends when the indentation depth increases, and the ISE impact almost disappears afterwards (Fig. 6a). Notably, the storage modulus is much higher than the loss modulus (Fig. 6b), as the value of tanδ is < 0.05 (Fig. 6c), which indicates that there was mainly elastic deformation within solid bitumen during loading process. Good linear relationships (0.68 < R2 < 0.98) are found among different mechanical parameters (Fig. 7a–c). 3.3. Creep behaviors Representative load-displacement curves (Fig. 8 a and b) and creep displacement-time curves (Fig. 8a′ and b′) are selected to show the creep behavior of solid bitumen. To facilitate the comparison among creep curves, the starting points for different tests are aligned, that is

Fig. 3. Typical Raman spectrum for solid bitumen (peak D 1326.2 cm−1 and peak G 1602.3 cm−1). 4

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Fig. 5. Typical load-displacement (a), load-time and displacement-time (b) curves of DMA mode. Parts of the loading curves in (a) and (b) are zoomed in to show the oscillation details.

related to the loading rate (Fig. 9b″).

the (0,0) point is the time that the holding period began, while the end point is the time that the holding period ended. The creep curves only exhibit transient and stationary stages without the accelerating one, indicating the load (stress) applied and time scale didn't exceed the yield strength (Zhao et al., 2018). The dependences of Young's modulus, hardness, We/Wt (We and Wt are the elastic work and total work, respectively, during indentation), creep displacement and its proportion to hmax on indentation depth and loading strain rate for all tests are shown in Fig. 9. Table 1 gives the statistical results for creep measurements.

4. Discussion 4.1. Mechanical properties The observations above indicate that the mechanical properties (Young's modulus and hardness) are influenced by both indentation size effect and indentation loading rate. 4.1.1. Indentation size effect Hardness is observed to decrease more significantly than elastic modulus as a result of surface stress distribution and work hardening (Wen et al., 2017). The most widely applied model to interpret ISE phenomenon is Nix-Gao model (Nix and Gao, 1998). This model is based on the strain gradient theory (Fleck et al., 1994), which suggests that ISE is a result of the changes of geometrically necessary dislocations density driven by the strain gradient in material. By combining Taylor's dislocation strengthening model and Von Mises flow rule, the relationship between the indentation hardness and displacement can be described as (Nix and Gao, 1998):

3.3.1. Different hmax with a fixed strain rate Fig. 8a displays representative load-displacement curves for tests with various hmax at a fixed strain rate of 0.05 s−1. According to the changing rate of displacement in Fig. 8a′, creep curves are divided into transient stage (first 10 s) and stationary stage (following period). During transient period, creep displacements for all tests increase but with a decreasing rate. At the following stage, it is notable that curves with hmax of 1000 nm, 1250 nm and 1500 nm exhibit negative variation rates, whereas those with larger maximum displacement set (hmax = 1750 nm, 2000 nm, 3000 nm and 4000 nm) have positive ones. This phenomenon indicates that a final penetration depth of ~1750 nm is the threshold depth, below which creep behavior could not happen. The changes of Young's modulus and hardness with indentation depth are shown in Fig. 9a. The values of these two parameters decrease slightly when hmax increased from 1000 nm to 2000 nm, whereas remained steady afterwards at around 7.8–7.5 GPa and 1.5–1.3 GPa, respectively (Fig. 9a, Table 1). This observation shows that the modulus of solid bitumen is fairly the same as the one for pyrolytic graphite (7.5 GPa) (Field and Swain, 1996).The proportion of elastic work to the total work is recorded to decrease with deeper penetration (Fig. 9a′), indicating more plastic deformation is made. And a deeper penetration generally leads to a larger creep displacement (Fig. 9a″). Notably, it is only when the hmax reached 4 μm, that a residual imprint, or a crack, can be occasionally seen on the surface after indentation (Fig. 10). Similar phenomenon was observed on the surface of graphite which only shows a damaged region rather than a symmetrically shaped indent hole after indentation (Richter et al., 2000).

H 2 = H0 2 + H0 2

h∗ h

(13)

where H is indentation hardness, H0 is the hardness that would arise from the statistically stored dislocations in the absence of strain gradient effects, h* is the characteristic length that characterizes the ISE depth, and h is indentation displacement. By plotting the linear relationship between H2 and 1/h, the ratio of the slope and intercept is equal to h*. Fig. 11a shows the plot of H2 and 1/h, as well as the fitting curve, from which H0 and h* are calculated to be 1.20 GPa and ~700 nm, respectively. Indentation size effect is significant for solid bitumen when the indentation depth is below ~700 nm, which is consistent with the experimental curve in Fig. 6a. In this view, in order to eliminate the influence form ISE for further creep tests, the maximum depth should be set no less than ~700 nm. Additionally, the plateau of Young's modulus starts from ~1500 nm of indentation depth (Fig. 6a). It implies that the Oliver-Pharr model is self-consistent from this indentation depth. This is important to identify the range of depth, within which the used Oliver-Pharr model is self-consistent, i.e., the modulus is independent of the indentation depth (Dokukin and Sokolov, 2012). Based on the results of ISE on hardness and elastic modulus, the maximum depth for creep tests is set to be larger than ~1500 nm. According to Milman et al. (2011), there is a power-law relation between nano-hardness and depth:

3.3.2. Different loading strain rates with a fixed hmax According to Fig. 8b, in order to reach the same final depth, a larger force is required when the loading rate is relatively slow. The plot of creep time-displacement (Fig. 8b′) for each curve reveals that the creep strain rate decreases during the first ~800 s in transient period, whereas remains constant at the following stationary period. It is obvious that a faster loading rate leads to smaller Young's modulus and hardness (Fig. 9b), whereas the variation of We/Wt over different rates is not significant (Fig. 9b′). The final creep displacement is positively

H = Ch−i 5

(14)

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Fig. 7. Correlations between the hardness and Young's modulus (a); storage modulus and loss modulus (b); Young's modulus between storage and loss modulus (c). Fig. 6. Corresponding changes of the mechanical properties as a function of displacement in Fig. 4. a Young's modulus and hardness; b Storage and loss modulus; c strain lag tanδ.

are ascribed to phase-transformation (Wang et al., 2006) and mechanical twinning (Karimpoor et al., 2003). The structure of solid bitumen is similar to but not as highly ordered as graphite. Graphite is highly ordered with atoms coordinated in sp3 bonded hexagonal sheets. These sheets are loosely bound to each other by Van der Waals forces, which makes graphite cleaved easily between the planes. The grain size of graphite structure is supposed to be 5–10 nm (Field and Swain, 1996). Being a kinking nonlinear elastic solid, the dislocations of graphite under indentation are confined to the basal planes, which do not entangle but can move reversibly over relatively large distances (Barsoum et al., 2004). Inter-planar slip in graphite are free to move in crystalline regions, and the slip in one area may cause the strain of inter-laminar bonds in adjacent domains, which is proven by the significant inter-laminar shearing response during indentation (Skinner and Gane, 1973). Molecular dynamics simulations during the indentation process have been performed on a highly oriented pyrolytic graphite sample, so as to study the mechanism of elastic deformation (Richter et al., 2000). Richter et al. (2000) suggests that a pure elastic deformation occurs with the bending of carbon lattice in graphite during indentation process. The bonds that connect the

where H is hardness, C is a constant, and i is the power-law exponent which implies the degree of indentation size effect. By taking the logarithm on both side of Eq. (14) and plotting the relationship between lgH and lgh, the absolute value of the slope is i. Previous studies about metal materials suggest i varies from 0.12 to 0.32 (Manika and Maniks, 2006). And the value of i for solid bitumen is calculated to be 0.26 by curve fitting (Fig. 11b). Generally, a larger value of i indicates a higher plasticity of the material.

4.1.2. Loading rate sensitivity The mechanical properties, including Young's modulus and hardness, of solid bitumen exhibit a negative loading rate sensitivity behavior under nanoindentation, that is a higher strain rate would result in a lower flow stress and tensile strength inside (Dowling, 1999). Such phenomenon has been observed in some nanostructured metallic materials (Karimpoor et al., 2003; Fan et al., 2006; Wang et al., 2006), and 6

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Fig. 8. Typical load-displacement curves (a), creep displacement and creep time curves (a’) for constant strain rate method with different hmax (1000, 1250, 1500, 1750, 2000, 3000 and 4000 nm) at the loading stain rate Ṗ/P of 0.05 s−1; the load-displacement curves (b), creep displacement and creep time curves (b′) for constant strain rate method with different strain rates Ṗ/PṖ/P (0.005, 0.01, 0.03, 0.07 and 0.1 s−1) at hmax of 3 μm.

(Fig. 12d). The creep processes from the upper right to the down left in Fig. 12d, during which time stress and strain rate decrease simultaneously. The linear part of the curve identified with the red triangle in Fig. 12d, is utilized for m calculation, which is 0.0098. Same calculation method was applied to obtain m at other experimental sets (Table 1). The variations of m with indentation depth and loading rate are plotted in Fig. 13a and b, respectively, which indicates the creep behavior of solid bitumen is weakly sensitive to indentation depth and loading strain rate.

interface of carbon atomic layers break under the loading, and recover as soon as the interface is extracted during unloading. No broken down is observed after unloading period, but only some small displacement of the atoms from their original positions in the lattices. Similar to graphite, the elastic deformation mechanism of carbon fiber under indentation is suggested to be associated with inter-layer kinking, buckling and shearing of crystallites (Ozcan et al., 2009), or full reversible incipient kink bands (Barsoum et al., 2004). In this view, the negative loading rate sensitivity for solid bitumen observed in this study may be attributed to the mechanical buckling and shearing of highly ordered aromatic carbons, of which the deformation mechanism is analogy to graphite (Karimpoor et al., 2003).

4.2.1. Indentation size effect The corresponding m derived is slight influenced by ISE, which remains constant at 1750 nm and 2000 nm, whereas rising sharply afterwards (Fig. 13a). Theoretically, creep strain rate sensitivity could imply the possible deformation mechanism for creep deformation. Previous study suggests that m being significantly < 0.25 indicates a dislocation power-law creep mechanism (Zhao et al., 2018). The extremely small m value in this study indicates that there was a strong localized shear flow inside solid bitumen when compressed during loading stage, and the deformation behavior is controlled by edge and mixed dislocations (Cheng et al., 2013), which is supposed to occur in graphite (Kelly, 1981). Besides, for metallic materials, the value of m is found to be positively related with grain size, as the edge and mixed dislocations density increases with decreasing grain size, whereas the screw dislocation density shows a reverse trend (Cheng et al., 2013). The grain size of graphite structure is rather small, being 5–10 nm. Assuming the structure of solid bitumen being similar to the one of graphite, the small grain size may be an important factor interpreting a rather small value of m in this study. According to free volume theory or shear transformation zone (STZ) theory, the weak positive dependence of m derived in this study upon indentation size may be due to the free volume generated under high

4.2. Creep behaviors The creep displacement-time curves during holding time stage is formulated by using the empirical Eq. (15) (Wu et al., 2016a):

h = a (t − b)c + d + et

(15)

where h and t are the creep displacement and creep time, respectively. Parameters a, b, c, d and e can be obtained by minimizing the sum of the squared differences between the squares of the measured and calculated displacement. Fig. 12a shows the typical experimental and fitted displacementtime curves during holding stage by using Eq. (15). The creep strain rate (ε )̇ and stress (σ) can be calculated by applying Eq. (9)–(10) (Fig. 12b and c). The value of ε ̇ decreases sharply from 0.0011 s−1 to 0.00009 s−1 during the first 20 s, after which the value remains constant at the stationary creep stage (Fig. 12b). In order to obtain the creep strain rate sensitivity during stationary stage, the flat part after the first 20 s was used for m calculation. Then the logarithmic plot of ε ̇ vs. σ and the creep strain rate sensitivity could be obtained by applying Eqs. (11)–(12) 7

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Fig. 9. Dependence of Young's modulus and hardness, We/Wt (We and Wt are elastic and total work respectively), creep displacement and its proportion to hmax on indentation depth (a, a′ and a″) and loading strain rate (b, b′ and b″). Each point is the average of 10 tests with standard deviation error bar.

deformation could be stored within the sample under higher loading rate, which would furtherly be converted into the plastic deformation during following holding period. Comparatively, the value of m only weakly depends on loading rate. As shown in Fig. 13b, m remains steady when indentation strain rate rises from 0.005 s−1 to 0.03 s−1, whereas increasing slightly at 0.07 s−1, after which becoming almost constant again. The general increasing trend may be explained by the interplay of the contributions of the Peierls stress and the dislocation density hardening to the flow stress (Alkorta et al., 2008). Even though the dependences of m on indentation depth and loading rate have been characterized, the observations obtained are subject to large errors arising from small variations of the results, which makes it hard to reach a robust conclusion. The mechanisms controlling the creep deformation of solid bitumen are still unclear, and more intensive investigation is required.

peak load (Li et al., 2019). In STZ theory, a local rearrangement of atoms occurs so as to accommodate shear strain caused by indentation. When the applied stress is above the yield stress, the movement of STZ will cause a local dilatation and shear bands within the free volume, which may further induce the local softening and the applied strain relaxing of the material. It is generally believed that the increasing peak load will result in a corresponding increasing volume of the “free volume” or “shear transformation zone” in the structure, which will cause a change of stress exponent. The more free volume is produced, the higher strain rate sensitivity is (Li et al., 2019). 4.2.2. Loading rate sensitivity In order to eliminate the ISE of mechanics on sample surface and the uncertainty for measurement from extreme deep indentations, tests at hmax = 3 μm with different strain rates are appropriate to analyze the loading rate sensitivity for creep behavior. The creep displacement is monitored to show a strong positive loading rate sensitivity (Fig. 9b″), and can be explained as: more elastic 8

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0.0008 0.0019 0.0055 0.0063 0.0003 0.0003 0.0002 0.0009 0.0014 0.0016 0.0041 0.0039 0.0099 0.0123 0.0008 0.0014 0.0016 0.0025 0.0037 0.0032

0.06 0.06 0.06 0.05 0.05 0.03 0.02 0.04 0.02 0.03 0.02 0.02 0.02 1.54 1.51 1.44 1.42 1.39 1.33 1.30 1.63 1.58 1.52 1.42 1.36 1.40 0.25 0.22 0.17 0.14 0.21 0.13 0.14 0.28 0.28 0.24 0.17 0.22 0.16

/

Ave. Std. Ave. Std.

Std.

Creep strain rate sensitivity Hardness (GPa)

8.12 8.05 7.92 7.83 7.76 7.63 7.57 7.88 7.73 7.62 7.56 7.42 7.36 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

In spite of the unavailability of inch sized solid bitumen sample, which is the standard sample volume for compression test, nanoindentation test on a sample at millimeter scale still provides us with a fundamental understanding of the creep behavior of organic matter in shale. However, this project only involves pure organic matter at fine scale, which is not our final goal. The upcoming questions are 1) what the creep deformations of inorganic phases, especially clay minerals, are like under nanoindenter, 2) how the bulk rock behaves during creep when small constituents with different phases (organic matter and minerals) are put together, 3) and whether indentation testing can be a satisfactory substitute for bulk test when the latter one is either unavailable or unusable on the material. Shales with more organic matter and clayish matrix are more compliant, and thereby favors creep deformation. Scenarios for shale creep during loading are supposed as: organic matter is no longer a perfect solid which flows under stress; and the piled-up clay plates slide on each other, thereby leading to interlayer friction (Mighani et al., 2015). Ranking as the second most compliant phase (the first one is organic matter) in shales, clay mineral, another contributor for shale creep deformation, is the next object of which the creep behavior at fine scale needs extensive investigation (Goldsby et al., 2004). Several studies have dealt with creep properties of bulk shale samples at nano/ microscale with the application of grid nanoindentation and deconvolution method (Mighani et al., 2015; Liu et al., 2018a; Sharma et al., 2019). Based on the investigation above, in the future, more efforts need to be devoted to relating these small-scale observations to macroscale testing, even in-situ shale reservoir conditions. Owing to the big difference of loading geometry and boundary condition between nanoindenter and compression test, whether results obtained from these two methods are comparable still remains unclear (Mighani et al., 2019). The stress level under indenter is roughly an order of magnitude higher than that for compression test on bulk specimens (Leslie et al., 2017). This is due to the fact that the stress under an indenter decreases gradually from high levels in the vicinity of the tip to small values in remote regions (and the same trend for strain), which is quite different from the effective stress commonly applied in conventional compression tests (Goodall and Clyne, 2006). For example, the stress (σ) calculated by Eq. (10) in Fig. 12 generally ranges from 452 MPa to 463 MPa, whereas the maximum axial stress loaded in conventional compression test is usually set at dozens of million pascal (Barsoum et al., 2004). But still, a few comparisons of the creep behavior for viscoelastic materials between nanoindentation and conventional compression test have been done. It is observed that for homogeneous materials (metallic and dental materials), the results obtained from two methods are in good agreement (El-Safty et al., 2012; Takagi et al., 2014). Whereas the study about heterogeneous shales suggested a spatial scale dependence of creep moduli, as the magnitude of mechanical properties obtained tends to correlate with the corresponding volumes of samples used at different scales (Mighani

1200 0.005 0.01 0.03 0.05 0.07 0.1

hmax: the maximum indentation depth; Pmax: the maximum loading force; We: the elastic work; Wp: the plastic work.

1.5 2.2 2.5 3.8 3.2 3.6 3.4 3.8 4.4 4.3 14.2 18.0 35.9 64.8 62.7 72.3 77.8 83.5 92.3 96.8

0.8 0.9 1.2 1.6 2.1 2.4 2.6 2.8 3.1 3.2

/ / / /

4.7 4.2 4.5 4.3 3.0 2.5 2.2 3.2 3.5 2.4 1.8 2.1 1.7 84.2 80.9 81.6 78.3 77.5 76.3 72.8 71.3 71.1 70.5 70.0 70.3 68.4 554 827 1002 1283 1025 5779 6303 6932 6617 6039 5992 5122 5327 4301 7388 14,215 22,929 31,922 104,155 237,631 125,668 119,209 114,502 106,182 101,222 88,586 129 187 244 256 539 372 730 3057 2883 2534 2204 2012 2212 681 1409 2618 4979 7182 24,642 64,625 36,064 34,502 33,771 31,905 30,037 28,001 157 321 527 579 1028 6152 5573 4003 3791 3282 2938 3002 2983 3620 5979 11,597 17,949 24,740 79,513 173,005 89,604 84,707 80,731 74,277 71,185 60,585 0.3 0.2 0.5 0.4 0.7 1.9 3.7 3.1 3.6 3.4 2.6 2.3 2.2 12.6 17.5 27.5 37.2 45.3 97.6 168.6 106.1 102.1 101.1 95.6 91.9 79.1 100 0.05

1000 1250 1500 1750 2000 3000 4000 3000

Ave. Std. Ave. Std. Ave. Std. Ave. Std. Ave.

Std.

Ave.

Std.

Ave.

Std.

Ave.

Young's Modulus (GPa) Creep displacement/ hmax (%) Creep displacement (nm) We/ Wt (%) Wt (pJ) Wp (pJ) We (pJ) Pmax (mN) Pause in load (s)

hmax (nm)

Fig. 10. Optical micrograph of solid bitumen before (a) and after (b) nanoindentation for test at the strain rate of Ṗ/P 0.05 s−1 with hmax = 4 μm.

4.3. Limitations and implications for further work

Loading strain rate (s−1)

Table 1 Results for nanoindentation tests by using different methods.

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Fig. 11. Dependence of H^2 on h−1 (a) and ln H on ln h (b) for solid bitumen (H is hardness and h is indentation depth).

based on nanoindentation with only metric samples would gradually be standardized and substitute the conventional compression test. This microscale approach could update rock models for underground dynamics, thereby optimizing drilling and hydraulic fracturing design, and the evaluation of reservoir productivity during shale gas depletion in South China.

et al., 2019). After a fully understanding of creep deformation for individual constitute, a model by which nanoindentation measurement can be upscaled and then compared to triaxial compression test needs to be established. As it is introduced in the Section 1, the prediction of multiscale mechanical performances of organic rich shales in South China is intricate due to their complicated chemistry and heterogeneous microstructure. Thus, consideration of mineralogy and microstructure, including composition, porosity, particle size distribution etc., is essential for the development of fine scale predictive model, which could overcome the demand for costly and time-consuming compression experiments, to access bulk mechanical behavior. In conclusion, after systematic confirmation of the validity, method

5. Conclusions By evaluating the mechanical properties and creep behavior of solid bitumen via nanoindentation test, their sensitivities to indentation size and loading rate were, for the first time, systematically investigated. The deformation of solid bitumen under indenter is analogic to

Fig. 12. The creep displacement-time curve during holding stage (a), creep strain rate variation during creep time (b), stress variation during creep time (c), and double logarithmic plot of stress versus creep strain rate (d) at the strain rate of 0.05 s−1 with hmax = 3 μm and a pausing time of 100 s. 10

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Fig. 13. Creep strain rate sensitivity plotted as a function of penetration depth with a loading rate of 0.05 s−1(a) and loading strain rate with a hmax of 3 μm (b) (mean with standard deviation error bar).

graphite. Mechanical properties, including hardness and Young's modulus, are observed to be negatively influenced by indentation depth and loading rate, which may be attributed to the deformation of aromatic carbons in solid bitumen. Creep strain rate sensitivity (m) shows weak sensitivity to indentation depth and loading rate. That is, the value of m increases slightly along with increasing depth, of which the deformation mechanism could be explained by shear transformation zone in aliphatic carbons; and a faster loading rate generally leads to a larger m calculated. However, due to the large errors arising from small variations of the results, further investigation is prerequisite before drawing a robust conclusion. This study based on small sample size and time scale could shed light upon creep deformation of organic matter, whereas it is not our final goal. Next steps involve relating small-scale observations to the macro or even in-situ shale reservoir conditions. With the consideration of mineralogy and microstructure, convenient fine scale tests can lead to development of predictive models, which will substitute costly and time-consuming traditional experiments, to access bulk mechanical behavior.

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Declaration of Competing Interest We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled. Acknowledgements This work was financially supported by Special Fund for Strategic Priority Research Program of the Chinese Academy of Sciences (XDA14010102) and the National Natural Science Foundation of China (grant no. 41802165). The authors are grateful to Editor Dr. Karacan and anonymous reviewers for their instructive comments and suggestions that significantly help clarify this manuscript. And we appreciate the support from Dr. An Qi from Harbin Institute of Technology and Dr. Yu Shilun from Central South University for interpreting the creep data. References Alkorta, J., Martínez-Esnaola, J.M., Gil Sevillano, J., 2008. Critical examination of strainrate sensitivity measurement by nanoindentation methods: application to severely deformed niobium. Acta Mater. 56, 884–893. Barsoum, M.W., Murugaiah, A., Kalidindi, S.R., Zhen, T., Gogotsi, Y., 2004. Kink bands, nonlinear elasticity and nanoindentations in graphite. Carbon 42, 1435–1445. Bower, A.F., Fleck, N.A., Needleman, A., Ogbonna, N., 1993. Indentation of a power law creeping solid. Proc. R. Soc. A 441, 97–124.

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