Damage Mode and Energy Consumption Characteristics of Paper-Sludge-Doped Magnesium Chloride Cement Composites

Abstract

To reduce the pollution caused by paper sludge in the environment and overcome issues of poor water resistance and brittleness in Magnesium Oxychloride Cement (MOC), the MOC was modified by adding different dosages of paper sludge. The mechanical properties and damage modes of composite MOC materials containing paper sludge were studied by uniaxial compression tests. Under cyclic loading conditions, the damage progression of MOC composites was characterised using the tensile-shear conversion factor (Tsc) and by monitoring the energy parameters (elastic strain energy, plastic strain energy and dissipation energy). The results show that the average peak stress drop of MOC composites gradually increases with the increase in paper sludge dosage. Under uniaxial compression conditions, the Tsc of the MOC composites decreases from 0.99 to 0.44, and the damage mode is transitioned from brittle tensile damage to tensile-shear damage, X-shaped conjugate surface shear damage and finally to pure shear damage with an increase in doping. During cyclic loading conditions, the brittleness of MOC composites gradually decreases with an increase in paper sludge doping, which verifies the effect of paper sludge on the mechanical properties of MOC materials and the change in damage modes from the perspective of energy dissipation.

1. Introduction

In recent years, tens of thousands of tonnes of general industrial solid waste have been dumped and discarded in large and medium-sized cities in China. As the terminal waste of paper-making enterprises, paper sludge is mainly managed through sanitary landfilling within the industry. Due to the various treatment methods, the landfill will contain trace amounts of lead, copper, nickel, chromium and other heavy metals which can lead to secondary soil pollution. Moreover, landfill sludge occupies a large amount of agricultural land, which is not conducive to China’s adherence to the concept of green and sustainable development. As a result, China began to gradually implement refined and systematic treatments for paper sludge.

Some researchers have conducted related studies about paper sludge. For example, Chen et al. [1] compared the composition and properties of different paper sludges and found that the incorporation of paper sludge significantly reduced its thermal conductivity. Tofani et al. [2] evaluated the thermal stability of the incinerated paper sludge by infrared analysis. Aiken et al. [3] revealed the crystalline structure, microscopic morphology and physical phase composition of each Magnesium Oxychloride Cement (MOC) building board and explored the feasibility of MOC building boards to replace traditional thin sheet materials, such as plywood, gypsum plasterboard and fibre cement board. Wang et al. [4] investigated the effects of fly ash and polyethylene fibre incorporation on the flow, tensile properties and compressive properties of MOC. Ye et al. [5] prepared corn starch/poly(sodium acrylate) (PAAS) MOC composites with higher compressive strength and water resistance. Gong et al. [6] investigated the effect of paper sludge with different dosages, particle sizes and water contents on the strength and microscopic properties of magnesium chloroxygenated cement by means of compressive strength test, water absorption test, SEM and XRD. Chen et al. [7] investigated the effect of phosphoric acid and tartaric acid addition on the water resistance of MOC cement pastes. Devi et al. [8] used waste paper sludge ash to replace M25 grade concrete at different percentages (2.5%, 5.0% and 7.5%), and they found that a 5% substitution rate yielded superior mechanical properties. Ingale et al. [9] comprehensively tested the mechanical and durability properties of the composites, and they finally achieved the best overall performance of the material at a 5–10% substitution rate. Gomes et al. [10] prepared magnesium chloroxylate fibre cement boards with different molar ratios, and they found that rice husk silica (RHS) increased the modulus of rupture and toughness of the MOFC and improved the durability of the material through the filler effect. He et al. [11] prepared straw/sawdust–magnesium chloroxylate cement composites (SMOCC) from straw, sawdust and MOC using a compression moulding process, and they found that increasing the compression pressure can effectively reduce the porosity to redistribute pore sizes, which resulted in an increase in compressive strength and flexural strength. Singh et al. [12] found that the calcination temperature, the bohemian of MgCl₂ solution, and the fineness of the filler were the key factors controlling the development of MOC strength.

Zhao et al. [13] used the phase inversion method to modify a novel polyvinyl chloride (PVC) membrane with graphene oxide (GO) to improve its hydrophilicity and mechanical properties. Yu et al. [14] found that the prepared high-performance MOC possessed high early strength, high ductility and good water resistance. Xu et al. [15] revealed that the changes in the microscopic properties of MOC cementitious composites induced by high-temperature curing are the macro-mechanical changes significantly. Liu et al. [16] conducted uniaxial compression cyclic loading and unloading tests at different rates and micro-morphological analysis of crack surfaces, showing that with an increase in loading and unloading rates, the energy evolution eventually changed from being dominated by the damping energy to being dominated by the damage energy. Rapid loading and unloading rates were the main factors contributing to the larger dissipation and damage energy in the rock. Meng et al. [17] and Liu et al. [18] investigated the effect of loading and unloading rates on the energy evolution and damage characteristics of rocks under cyclic loading using four rock samples, and they found that the dissipated energy increased nonlinearly with an increase in loading and unloading rates for all of them. Wang et al. [19] used the loading and unloading response ratio (LURR) to evaluate the cumulative damage of porous coal under cyclic loading. Wang et al. [20] proposed a micromechanical model of LWAC using the nearest surface distribution function, generalised self-consistent scheme and two-phase spherical model to analyse the damage process of lightweight shale vitrified concrete. Gao et al. [21] described the damage mechanism of tectonic coal from the perspective of energy distribution by introducing the concepts of crushing and friction energy. Xu et al. [22] analysed the energy, deformation and crack development mechanism of rubber-cemented mortar under three different cyclic loading and unloading modes, failure mode and crack development mechanism. Song et al. [23] demonstrated that material energy dissipation and damage evolution were related to the stress path. Lin et al. [24] found that the damage variables reached a stable growth stage with a gradual increase in loading and unloading cycles under different circumferential pressures by conducting triaxial unloading tests on salt rock specimens.

The above researchers mainly worked on the treatment of paper sludge, the improvement of water resistance of MOC composites and the study of solid waste fillers. They found that different substitution rates, molar ratios, filler finenesses and pressing processes affect the micro-morphology and mechanical properties of MOC composites. In order to improve the water resistance of MOC composites, some researchers have used a range of modifiers, such as phosphoric acid, citric acid, tartaric acid, phenyl propylene emulsions and solid waste fillers, to study their water resistance. Meanwhile, regarding the energy consumption of rock-based materials, other researchers have conducted in-depth studies on the energy loss of different types of rocks under cyclic loading. However, there is no substantial solution for the defects of MOC composites, such as brittleness and susceptibility to cracking.

In this study, the brittleness of MOC cementitious materials was improved by using components such as lignin fibres derived from industrial solid waste paper sludge as well as using tiny particle size fillers, analysing the changes in damage modes and characterising the different mechanical properties embodied in each loading stage, and describing the damage mechanism from the perspective of energy dissipation by combining the elastic strain energy, the plastic strain energy and the dissipation energy. Under the cyclic loading conditions, the energy parameters, such as stage elastic strain energy, stage plastic strain energy and stage dissipation energy, were analysed, and a new variable parameter, i.e., the tensile-shear conversion factor (Tsc), was introduced to further investigate the damage evolution of MOC composites. Compared with other related articles, further explorations in green utilisation of solid waste and material modification were made.

2. Materials and Methods

2.1. Material Preparation

Magnesium oxide with 65% activity was manufactured in Dashiqiao City, Liaoning Province, China. Magnesium chloride with 46.4% purity was obtained from Tianjin Tanggu Jinlun Salt Chemical Co., Tianjin, China. Paper sludge (PS) was obtained from Xinmi Paper Mill, Xinmi, China. The paper sludge (PS) was selected from a paper mill waste in Xinmi City, China. The basic physical and chemical properties of the raw materials are given in

Table 1. Chemical composition of magnesium oxide.

Component	MgO	IL	SiO2	CaO	Al2O3	Fe2O3	Activated MgO
Content (%)	86.04	5.50	5.33	2.02	0.50	0.61	63.50

and

Table 2. Chemical compositions of MgCl₂ ·6H₂O.

Component	MgCl2	Ca2+	SO42−	Water-Insoluble Substance	Pb	As	NH4+
Content (%)	46.9	0.09	0.12	0.01	1.0	0.5	37

. Data used in Table 1 and Table 2 were from manufacturers. The results of the XRD spectra of the paper sludge used in the experiments are shown in Figure 1. The blue line represents the diffraction pattern of XRD and the red line represents the standard card. XRD testing is conducted to analyse whether the composition of the paper sludge has an effect on the generation of phases 3 and 5 within the MOC material.

The paper sludge used in the test was first dried to remove excess moisture. It was processed into fragments using an overhead crusher. It was ground into fine particles and small fragments using a ball mill. Finally, it is completely pulverised into powder using a small dry mill with a diameter of 15 cm and a high-speed crusher. The crushed sludge powder was then sieved through a 200 mesh square hole sieve to obtain the 75 μm sludge powder required for the test. The whole process is shown in Figure 2.

A molar ratio of MgO:MgCl₂:H₂O = 7:1:15 was used for the experiments. MgCl₂·6H₂O crystals were mixed with water and stirred thoroughly until the liquid in the container was free of visible granular crystals. It was allowed to stand for 24 h at room temperature around 20 °C and slowly poured into a measuring cylinder along with the mixture, ensuring that the temperature of the test liquid remained around 20 °C. The Baume degree of the measured agent should be observed using the scale-level intersection angle of the liquid surface. If the measured temperature significantly deviates from 20 °C, correct the measured value accordingly.

2.2. Experiment Method

As shown in Figure 3, this experiment considers paper sludge doping as the main variable. Firstly, 0%, 20%, 40%, 60% and 80% of paper sludge and magnesium oxide were weighed using an electronic balance. The dosage of paper sludge depended on the required strength, and when the dosage reached 80%, the strength decreased to a greater extent and the fluidity was poor; as a result, it was necessary to add a water-reducing agent. The practicality was poor, so higher dosage tests were not carried out. The dosage of paper sludge was measured based on the mass of magnesium oxide using the internal mixing method. The vertical mortar-concrete mixer manufactured in Cangzhou, China, was used for the experiment. Mixing was performed at a low speed for 120 s to ensure thorough mixing of the dry materials. After mixing for about 180 s, the concrete was quickly poured into a cylindrical iron mould with a diameter of 50 mm and a height of 100 mm. The moulds were removed and numbered after 28 d in a standard curing room. Then, the dry density test and static mechanical property test were carried out. Two strain gauges were affixed to the middle of each specimen’s side positioned symmetrically in both the transverse and longitudinal directions, and the stress–strain conditions were observed using the static strain gauges. In the multistage cyclic loading experiment, 20 kN was used as the loading increment interval. The loading rate and unloading rate were both 1 kN/s.

3. Results Analysis and Discussion

3.1. Variation Characteristics of Mechanical Parameters of MOC Composites

As shown in Figure 4, the initial state strength of the unblended paper sludge MOC material is high. With the increase in pressure, the primary pores and cracks within the MOC cement gradually healed. During the stage of compression and densification of the pore cracks, the modulus of elasticity of the material gradually tends to stabilise. The curvature of the curve presented by the material after compaction first becomes larger and starts to concave, as evident in the stress–strain curve of the 0%-doped MOC material. This stage has a greater effect on fractured rocks and a much smaller effect on materials with lower fracture and pore content and brittle materials. After the healing of the pores and fissures, the material gradually approaches a nearly straight elastic phase. At this stage, the pore cracks in the paper-mud composite MOC cementitious materials did not show significant compaction. This suggests that paper mud can indeed play a role in inhibiting the generation of pores and cracks.

In the elastic deformation phase, the stress–strain curve shows that the modulus of elasticity generally decreases with an increase in paper sludge dosage. When the dosage exceeds 20%, it will have an effect on the strength system generated by phases 3 and 5 within the composite MOC matrix. Excessive dosage produces a dilution effect. Figure 5 shows that the dry density of the MOC material increases with an increase in paper sludge dosage, but the decrease in compressive strength increases gradually, which confirms the above observation.

With further increases in pressure, the material progressed from the microelastic cleavage stable development stage to the elastic deformation limit stage. The characteristics of brittle materials began to manifest. The slope of the stress–strain curve of the specimen with uncompounded paper sludge still shows a small rate of change. It indicates that the elastic modulus of MOC material is basically stable in this process. In the case of composite paper sludge in the MOC material, it gradually shows a yield stage that is inconsistent with brittle materials. The 3D mapping surface plots of Poisson’s ratio, elastic modulus and compressive strength of MOC cement are shown in Figure 6. Figure 6 reveals the correlation between the elastic modulus as a response variable and the other two variables. The elastic modulus in the stress–strain curve can be regarded as the slope of the cut line at the instantaneous damage state point. The deterioration process of elastic modulus is actually a slow decrease in the slope of the cut line. Accompanied by the change in elastic modulus with step-by-step loading and unloading, the unloading modulus of the rock can also to some extent match the characterisation of the instantaneous elastic modulus of the damaged rock material under uniaxial compression. The Poisson’s ratio decreases to some extent from 0.27 to 0.22. The elastic phase also starts to end progressively earlier with the increase in dosage, and the later curve explains the earlier and earlier nature of the plastic material at the time of material damage under a high dosage of paper sludge. This stage produces a clear difference with the incorporation of paper sludge from the 0%-doped matrix. The brittleness of the material gradually decreases as the matrix reaches a 60% dosage, starting to produce significant plastic deformation. The plastic deformation is most pronounced at 80% doping.

The final breaking strength of MOC material is 100.35 MPa. The increase in dosage of paper sludge can help fill the pores within MOC cement. The pre-compaction stage of the material is shortened, and the material can enter the elastic stage to some extent faster when compressed, but the strength of the material decreases. The strength of the specimen decreased by 17.44% at 20% dosage. At 40% dosage, the strength decreased by 24.94%. At 60% dosage it decreased by 29.01%, and at 80% dosage strength decreased by 57.51%.

3.2. Transformation and Characterisation Methods for MOC Composite Damage Modes

The specimen has no obvious plastic changes in the preloading period. When reaching the destructive strength, the specimen shows complete destruction with an obvious popping sound due to the destruction. The edge of the specimen fragments splashes. The middle damage section is close to 90° showing a considerable number of rupture surfaces, such as Figure 7a and Figure 8a. There are multiple rupture surfaces in the middle running axially through the entire specimen. The rupture surfaces are smooth and flat. The middle part of the specimen mainly experiences tensile damage caused by the specimen exceeding the ultimate tensile strength of the material. However, a small amount of less pronounced shear damage still exists at its edges. Specimens doped with 0% paper sludge, under pressure, even hide the shear damage surface to some extent, which shows obvious tensile damage with the fracture surface of brittle material parallel to the axial direction. Although minor shear damage is still present on the lateral side of the specimen, it accounts for a relatively small amount compared to the main damage. What is presented in the figure belongs to the typical tensile damage of rocks. Due to the greater brittleness as well as the higher strength of the magnesium chlorite cementitious material, the final damage generates more energy. The specimen is damaged by peeling off from the outer wall in a split second. The damage depends on the material being subjected to tensile stresses exceeding the maximum stress limit due to the “Poisson effect”.

The damage pattern of magnesium chloroxylate cement specimens in the presence of 20%-doped paper sludge was altered. Compared to the 0%-doped specimens that incurred damage upon reaching the tensile stress limit, the 20%-doped edges still showed axial tensile damage, corresponding to Figure 7b and Figure 8b. The shear fracture surface inside the specimen close the end shows preliminary shear damage. However, the slip surface of shear damage is less obvious. The centre is still showing tensile damage, which indicates that the damage pattern of the material is gradually changing with the change in doping.

The axial compression of the composite MOC specimens with 40% doping resulted in significant changes in the damage slip surface. At the end of the specimen, there appeared a localised conical surface as shown in Figure 7c and Figure 8c. The angle between the damage section and the horizontal plane also changed to different degrees. This explains that the damage mode of the specimen is gradually changing. The ratio of tensile damage and shear damage is converted to some extent. The tensile damage is gradually converted to shear damage.

The strength of the material decreased as the paper sludge doping increased. Unlike the previous damage pattern, the specimens at 60% dosage no longer showed high-energy specimen bursting. The sides still show tensile damage as shown in Figure 7d and Figure 8d. However, the fragmentation of the sidewalls is no longer towards the fragmentation demonstrated at small dosages. The parts resulting from tensile damage tend to be increasingly monolithic. The X-shaped conjugate shear damage occurs within the composite MOC material, and the localised conical surfaces appear at the upper and lower ends. The two cone-shaped vertices are almost connected. The tensile damage on the sides no longer appears fragmented, but increasingly shows a trend towards wholeness.

Finally, the specimen at 80% paper sludge doping showed obvious plasticity changes in the early stage. The plasticity showed a significant enhancement. The damage is manifested in the specimen extending from the end of the diagonal shear surface through the specimen, as shown in Figure 7e and Figure 8e. The damage surface is rougher at this point, which is different from the smoother tensile damage surface presented by the 0%-doping specimen.

The tensile-shear damage of rock is a form of combined rupture based on the nature of the material, which is subjected to normal tensile stress perpendicular to the axial compression direction and also damage from shear force horizontal to the rupture surface at the same time. This phenomenon is mainly explained by the third strength theory proposed by Coulomb. In rock mechanics, this theory is often applied to the study of various engineering problems related to the description of rocks damaged by shear. Coulomb’s law states that when we study the shear damage of rocks, we address two main aspects. One is the bond between rock and soil particles, and the other part is the internal friction which is positively related to the positive stress. The angle of internal friction is between different levels within the rock. The maximum shear stress at which a rock resists damage by shear is called shear strength. The shear strength of rock, like that of soil, is also composed of two parts, cohesion and internal friction resistance, both of which are larger than that of soil, which is related to the fact that rock has a strong connection.

By collecting and reassembling the specimen fragments at different doping levels in each group and analysing the damage cross-section, the internal tensile strength of MOC composites was simulated by using revit modelling software. Combined with the actual cross-sectional damage morphology of MOC composites, the revit modelling software was used to simulate the internal perspective of tensile-shear damage within MOC composites at five doping levels: 0%, 20%, 40%, 60% and 80% (Figure 9I–V). The characteristics of the damage pattern changing with the doping amount and the energy dissipation in the whole process are combined to jointly corroborate the damage evolution law of MOC composites.

The following equations were introduced to calculate the actual various mechanical damage parameters of MOC:

$${\epsilon }_{max1}=\mu {\epsilon }_{max2}$$

(1)

where ε_max1 is the transverse ultimate strains corresponding to MOC composites. ε_max2 is the longitudinal ultimate strains corresponding to MOC composites. μ is the Poisson’s ratio corresponding to MOC composites.

$${\sigma }_a=E{\epsilon }_{max1}$$

(2)

where E is the modulus of elasticity of the material at different dosages. σ_a is the ultimate tensile stress of the material at different dosages.

$$\alpha =\frac{\mathsf{\pi }}{4}+\frac{\phi }{2}$$

(3)

where α is the angle between the surface of destruction of the material and the horizontal plane. φ is the angle of internal friction of the material.

$${\sigma }_n={\sigma }_x{\mathrm{c}\mathrm{o}\mathrm{s}}^2\alpha +{\sigma }_y{\mathrm{s}\mathrm{i}\mathrm{n}}^2\alpha -2{\tau }_{yx}\mathrm{s}\mathrm{i}\mathrm{n}\alpha \mathrm{c}\mathrm{o}\mathrm{s}\alpha$$

(4)

$${\tau }_n=\left({\sigma }_x-{\sigma }_y\right)\mathrm{c}\mathrm{o}\mathrm{s}\alpha \mathrm{s}\mathrm{i}\mathrm{n}\alpha +{\tau }_{xy}\left({\mathrm{c}\mathrm{o}\mathrm{s}}^2\alpha -{\mathrm{s}\mathrm{i}\mathrm{n}}^2\alpha \right)$$

(5)

where σ_x is the longitudinal stresses received by MOC composites. σ_y is the transverse stresses on MOC composites. σ_n is the positive stress perpendicular to the damage surface of the material.

$$C=\frac{{\sigma }_n(1-\mathrm{s}\mathrm{i}\mathrm{n}\phi )}{2\mathrm{c}\mathrm{o}\mathrm{s}\phi }$$

(6)

where C is the internal cohesion of the material.

$$\tau =C+{\sigma }_n\mathrm{t}\mathrm{a}\mathrm{n}\phi$$

(7)

where τ is the actual shear force on the damage surface.

The mechanical parameters of the composite MOC material calculated from the above equations are listed in

Table 3. Mechanical parameters of MOC composites.

Paper Sludge Content (%)	0%	20%	40%	60%	80%
σa (MPa)	29.26	26.00	25.24	20.01	10.20
α (°)	/	65.5	58.0	61.0	63.4
Φ (°)	/	41.1	26.0	31.9	36.9
C (MPa)	/	28.38	42.30	33.57	17.06
τ (MPa)	/	36.87	52.62	44.018	23.45
Tsc	0.99	0.669	0.480	0.455	0.435

.

The characteristics of the different damage modes of MOC were analysed by introducing the tensile-shear conversion factor (Tsc) as shown in Figure 10. Based on the damage modes, it is broadly classified into three stages. In the initial damage stage of MOC composites, the change from tensile to shear conversion rate exhibited by the tensile-shear conversion factor from the first stage to the second stage is high. This stage corresponds to a high variation in material compressive strength from 100.35 MPa to 82.85 MPa. The specimen undergoes the compaction of the natural pores within the specimen and the gradual healing of the cracks leading to the generation of nascent cracks. The material’s tensile-shear conversion factor starts to accumulate at this stage of the damage. The Tsc index decreases from 0.99 to 0.66. The second stage of damage is persistent uniform damage. The fracture compaction process reduces the energy lost in the process due to the addition of a certain amount of paper sludge to fill the internal porosity.

The Tsc index decreases from 0.67 to 0.46, indicating that the damage of the 20%, 40% and 60% MOC composites develops in a slow incremental progression. The change in slope is relatively small. The compressive strength decreases from 82.84 MPa to 71.19 MPa, indicating that the compressive damage mode of MOC materials in the 20–60% doping interval is mainly tensile and shear combined damage. However, the influence ratios are not the same when leading to the damage. The material damage accumulates faster when the Tsc index is from 0.455 to 0.435. The deformation during loading is more obvious compared to other dosages. The final compressive strength decreased from 71.19 MPa to 42.63 MPa. The decrease in compressive strength at this stage was relatively large, which is due to the substantial reduction in paper sludge within the strength structure of the 3-phase and 5-phase proportions, resulting in the more obvious “dilution effect” on the overall performance. At this time, the specimen will not show violent brittle damage. In the case of the 80%-doped MOC specimens, the crack expansion rate is slower. The mechanical properties of MOC materials exhibited in these three stages are very different, which is useful for future experiments in the modification of MOC cement.

3.3. Cyclic Loading and Unloading Experimental Methods and the Curves for MOC Composites

A universal testing machine was used to test the mechanical performance of MOC cementitious materials under cyclic loading with different paper sludge dosages. The ultimate stresses of MOC materials with different dosages under actual uniaxial loading were selected. Finally, a loading interval of 20 kN was adopted as the standard for adjusting cyclic loading. After the loading and unloading applications were debugged and stabilised, the standard specimens were placed on the experimental bench to start cyclic loading.

The mechanical properties of MOC materials subjected to cyclic loading were significantly changed by changing the dosage of paper sludge. The total energy input, elastic strain energy, plastic strain energy, dissipation energy, residual deformation and other parameters measuring the material damage during the loading process also showed obvious regularity. The maximum loading times and cyclic loading paths corresponding to uniaxial graded loading are shown in Figure 11a,b.

3.4. Energy Evolution and Damage Characterisation Based on MOC Composites

The deformation, damage and destruction processes of MOC composites are accompanied by complex energy changes. The total energy input and loss of the system can serve as important factors for measuring and responding to the internal accumulation of material damage. The process includes the healing of the primary cracks of the original MOC composites, the generation of nascent cracks, the stage of the nascent cracks development and the eventual damage caused by the original MOC composites. According to the law of energy conservation, the energy input from the external load is referred to as the total energy W₁, and the total energy exerted by the whole test system on the MOC material under cyclic loading has the following energy relationship:

$$W_1=E_d+E_e$$

(8)

$$E_d=E_p+E_1$$

(9)

$$W_1={\int }_{{ϵ}_0}^{{ϵ}_2}{\sigma }_x\mathrm{d}ϵ$$

(10)

$$E_d={\int }_{{ϵ}_1}^{{ϵ}_2}{\sigma }_y\mathrm{d}ϵ$$

(11)

Figure 12a represents the loading and unloading situation in a certain stage. σ_x is the instantaneous stress corresponding to the loading curve under the cyclic loading and unloading stages. σ_y is the instantaneous stress corresponding to the unloading curve under the cyclic loading and unloading stages. W₁ is the total energy inputted by the whole test system in this stage as shown in Figure 12b, which is obtained by integrating the loading curve and the area enclosed by the transverse strain in this stage. Ee is the elastic strain energy stored within the specimen, which denotes the strain energy that is present within the specimen and can be released, as shown in Figure 12c. It is obtained by integrating over the unloading curve and the area enclosed by the transverse strain at this stage. E_d is the total energy loss generated during cyclic loading and unloading of the platform, which is obtained by subtracting the elastic strain energy from the integral over the region of the total energy input to the platform. E_p is the plastic strain energy used for plastic deformation during loading and unloading, as shown in Figure 12d, which is obtained by subtracting the total input energy for the next stage of loading from the total energy dissipated during that stage of loading and unloading. E₁ is the actual energy dissipated during loading and unloading, as shown in Figure 12e. The plastic strain energy resulting from plastic strain is subtracted from the total dissipated energy.

In the unloading process, part of the deformation will be recovered as elastic deformation. The energy accumulated at this stage is the elastic strain energy. On the other hand, the remaining unrecoverable deformation is the residual deformation of the composite MOC material during the process. This is caused by the closure, slip and misalignment of the structural surfaces of the MOC material during the axial compression. Dissipated energy includes energy in the form of heat during cyclic loading and unloading and energy consumed by internal damage destruction. The elastic strain energy at each stage of loading increases with the number of loading cycles. This results in more thermal energy being lost during the process, and more energy is consumed due to internal damage. The cyclic loading curve produces less energy consumption due to the inelastic deformation of the structural surfaces compared to a typical rock. The overall curve is still consistent with the characteristics of brittle materials under pressure. There is no significant plastic deformation observed during the loading and unloading phases.

With the increase in the number of cyclic loading, the elastic strain energy, plastic strain energy and dissipated energy all showed a gradual increase in the MOC composites with 0% doping. At a paper sludge dosage of 40%, the average plastic strain energy per cycle in the unloading stage of the curve starts to increase compared to the average plastic strain energy per cycle at 0% and 20%. As the paper sludge dosage increases, the peak value of the envelope decreases. The residual strain also increases with an increase in plastic strain energy. The overall brittleness of the specimens was reduced and the plasticity was improved to some extent.

As shown in

Table 4. Energy of MOC composites under cyclic loading at different dosages.

Paper Sludge Content (%)	Total Energy (MJ·m−3)	Elastic Strain Energy (MJ·m−3)	Plastic Strain Energy (MJ·m−3)	Dissipative Energy (MJ·m−3)	Residual Strain
0	1.635	1.471	0.091	0.073	0.0025
20	0.899	0.823	0.051	0.025	0.0035
40	0.679	0.867	0.085	0.044	0.0125
60	0.999	0.778	0.166	0.072	0.0078
80	0.056	0.043	0.006	0.015	0.0066

and Figure 13, most of the energy dissipation generated at each level of the loading stage in MOC is attributed to plastic deformation with a small amount of heat energy dissipation. As the plastic deformation and residual strain increase in each stage, the cumulative damage reflected in the MOC composites is larger. Different average dissipation energies result in different levels of damage, and as a result, different damage modes occur. Before reaching the ultimate stress yield point of the material, the material passes through a compaction phase. The damage caused by this stage is mainly due to the primary state of the internal micro-cracks resulting from repeated compaction and crack healing damage. This damage is more obvious when the paper sludge is not mixed. The internal microporosity is higher than that of the paper sludge, which is the absolute damage in the early stage. As the cyclic loading test force increases, new cracks begin to appear in the MOC material. This marks the beginning of the accumulation of damage in the second stage of the material. Starting from the first loading, the average elastic strain energy of the loading stage gradually decreased. The properties of the MOC material were analysed from the perspective of energy loss under cyclic loading and from the mechanical point of view through Tsc, and the changes in the damage modes of paper sludge with different dosages were confirmed.

4. Conclusions

The paper sludge was used to change the brittleness of MOC composites by varying its dosage. The uniaxial compression experiments and cyclic loading mechanical experiments were carried out. The Tsc was introduced to further analyse the damage mechanism from both the mechanical and the energy loss perspectives. The mechanical properties and damage mechanisms of MOC composites were studied with the increase in paper sludge dosage. The following conclusions were drawn:

(1) The modulus of elasticity of MOC gradually decreases from 13.30 GPa to 8.04 GPa with the increase in paper clay doping. Poisson’s ratio also decreases to a certain extent within a small range of 0.27–0.22, which indicates that the proportion of transverse and longitudinal strains generated by uniaxial compression of MOC decreases at different doping levels. MOC can be reasonably substituted for conventional silicate cement without affecting the actual applied strength. This not only improves its mechanical properties but also reduces the cost of disposal of this industrial solid waste and improves the environment.

(2) In the process of increasing the doping level from 20% to 60%, the damage mode gradually shifts from tensile damage to tensile-shear conjugate damage mode. The proportion of tensile damage in the damage process is gradually decreasing. Subsequently, the tensile-shear combined damage is over to X-shaped conjugate shear damage and finally becomes pure shear damage. To characterise the changes in damage patterns, a tensile-shear conversion factor (Tsc) was introduced, which is of significance for the subsequent study of the damage mechanism of MOC materials.

(3) With the increase in sludge dosage, the elastic strain energy under the loading and unloading stages gradually decreases, and the plastic strain energy, dissipation energy and residual strain increase to different degrees. Since different MOC materials can withstand different numbers of loading and unloading, it is suggested that the elastic strain energy, plastic strain energy and dissipation energy at each stage of the loading and unloading process should be used to reveal the ratio of the energy of a particular loading stage to the overall damage process.

Based on the modification of MOC composites using different amounts of paper sludge, the sludge after high-temperature calcination has the characteristics of volcanic ash. The next stage is expected to carry out more in-depth research on MOC materials by calcining paper sludge under different temperature gradients and adjusting the particle size of paper sludge. In the experiment, the acoustic emission sensors and other detection instruments will be used to further investigate the crack expansion pattern of MOC composites.